a square with a side length of 4.9 10-9 m, each with mass 1.7×10⁻²⁷ kg and charge 1.6×10⁻¹⁹ C. And they are let go of their sleep. When the protons are very far apart, the speed of each proton is 7.0e5 m/s.
We can start by finding the initial potential energy of the system when the four protons are held at the corners of the square. The potential energy is given by:
U_i = (1/4πε₀) * (q₁q₂/r)
where ε₀ is the permittivity of free space, q₁, and q₂ are the charges of the two protons, and r is the distance between them.
Since all four protons are identical and equidistant, we can calculate the initial potential energy of the system by summing up the potential energies of each pair of protons:
U_i = 2 * [(1/4πε₀) * ((1.6e-19 C)² / (4.9e-9 m))] + 2 * [(1/4πε₀) * ((1.6e-19 C)² / (4.9e-9 m * √2))]
where the factor of 2 in front of each term takes into account the fact that there are two pairs of protons.
Evaluating this expression gives U_i = 1.55e-17 J.
At infinite separation, the potential energy of the system will be zero, and all of the initial potential energy will have been converted into kinetic energy. Therefore, we can use the conservation of energy to find the speed of each proton when they are very far apart:
U_i = K_f
where K_f is the final kinetic energy of the system.
K_f = (1/2) * m * v²
where m is the mass of a proton, and v is its speed.
Setting U_i equal to K_f and solving for v gives:
v = √(2U_i/m)
Substituting the values we obtained earlier, we get:
v = √[(2 * 1.55e-17 J) / (1.7e-27 kg)]
v ≈ 7.0e5 m/s
Therefore, the speed of each proton when they are very far apart is approximately 7.0e5 m/s.
Learn more about protons here:
https://brainly.com/question/30895149
#SPJ4
two cars approach an ice-covered intersection. one car, of mass 1.27 103 kg, is initially traveling north at 11.6 m/s. the other car, of mass 1.70 103 kg, is initially traveling east at 11.6 m/s. the cars reach the intersection at the same instant, collide, and move off coupled together. find the velocity of the center of mass of the two-car system just after the collision.
The center of mass of the two-car system can be found by taking the weighted average of the velocities of the two cars.
The velocity of the center of mass is the average of the two cars' velocities, weighted by their masses. The velocity of the center of mass is:
Velocity of Center of Mass = (1.27 x 103 kg x 11.6 m/s + 1.70 x 103 kg x 11.6 m/s) / (1.27 x 103 kg + 1.70 x 103 kg) = 11.60 m/s.
Read more about the topic velocity:
https://brainly.com/question/80295?source=archive
#SPJ11
An engineer is designing the runway for an airport. Of the plane that will use the airport, the lowest acceleration rate is likely to be 3 m/s2 . The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway?
Answer:
Approximately [tex]705\; {\rm m}[/tex].
Explanation:
Let [tex]x[/tex] denote the distance travelled before the plane takes off.
Let [tex]u[/tex] denote the initial velocity of the plane, and let [tex]v[/tex] denote the velocity of the plane when it takes off. It is given that the takeoff speed is [tex]v = 65\; {\rm m\cdot s^{-1}}[/tex]. Assuming that the plane was initially stationary, initial velocity would be [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex].
It is given that the acceleration of the plane would be [tex]a = 3\; {\rm m\cdot s^{-2}}[/tex].
Since acceleration is constant, apply the SUVAT equation [tex]x = (v^{2} - u^{2}) / (2\, a)[/tex] to find the value of [tex]x[/tex]:
[tex]\begin{aligned} x &= \frac{v^{2} - u^{2}}{2\, a} \\ &= \frac{(65)^{2} - (0)^{2}}{2\, (3)}\; {\rm m} \\ &\approx 705\; {\rm m}\end{aligned}[/tex].
(Rounded up.)
Hence, the length of the runway should be at least [tex]705\; {\rm m}[/tex].
A magnifying glass with focal length 15 cm is placed 10 cm above a stamp. The image of the stamp is located a. 15 cm from the magnifying glass. b. 30 cm above the stamp. c. 30 cm above the magnifying glass. d. 30 cm below the stamp. e. 30 cm below the magnifying glass.
The image of the stamp when a magnifying glass with focal length 15 cm is placed 10 cm above a stamp is located 30 cm above the magnifying glass. The correct answer is Option C.
Let the object distance, u be -10cm (since the stamp is placed 10 cm above the magnifying glass).
Let the focal length of the lens, f be 15cm.
So, the magnification, m is given as:
m = v/u (where v is the image distance)
Using the lens formula, we can say that:
1/f = 1/v - 1/u (where v is the image distance and u is the object distance)
Plugging in the given values into the formula we have:
1/15 = 1/v + 1/10
Multiplying both sides of the equation by 30v, we have:
2v = 3(30 - v)
Solving for v, we have:
v = 30/2 = 15 cm
Since v is positive, it means that the image of the stamp is formed on the other side of the lens (on the side of the lens where the image of the stamp is formed, we measure the distance from the lens from this side). Hence, the image is located 15cm from the lens. Since the stamp is located 10 cm above the magnifying glass, the image of the stamp is located 15 + 10 = 25cm above the object or the magnifying glass. Thus, the correct option is c. 30 cm above the magnifying glass.
Learn more about magnification here: https://brainly.com/question/1599771
#SPJ11
A straight 2.80 m wire carries a typical household current of 1.50 A (in one direction) at a location where the earth's magnetic field is 0.550 gauss from south to north.
*I know there's a lot of questions, but I will rate the you-know-what out of you
a) Find the direction of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running from west to east.
b) Find the magnitude of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running from west to east.
c) Find the direction of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running vertically upward.
d) Find the magnitude of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running vertically upward.
e) Find the direction of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running from north to south.
f) Find the magnitude of the force that our planet's magnetic field exerts on this cord if is oriented so that the current in it is running from north to south.
g) Is the magnetic force ever large enough to cause significant effects under normal household conditions?
If the current is running from west to east, then the direction of the force that our planet's magnetic field exerts on the cord is from south to north directions and The magnitude of the magnetic force is about 0.825 Newtons.
What are the magnetic force?If the current is running from west to east, then the direction of the force that our planet's magnetic field exerts on the cord is from south to north. The magnitude of the force is given by the equation F = B × I × L, where B is the magnetic field strength, I is the current, and L is the length of the wire. In this case, the magnitude of the force is 0.825 N.
If the current is running vertically upward, then the direction of the force that our planet's magnetic field exerts on the cord is from east to west.
The magnitude of the force is again given by the equation F = B × I × L, so the magnitude of the force is 0.825 N.
If the current is running from north to south, then the direction of the force that our planet's magnetic field exerts on the cord is from west to east.
The magnitude of the force is again 0.825 N. The magnetic force is not large enough to cause significant effects under normal household conditions.
Learn more about Magnetic force here:
https://brainly.com/question/3160109
#SPJ11
joshua trees cannot germinate and grow as easily in today's warmer climate. which of these actions would be most likely to help the species survive climate change?
One of the actions that can be taken to help Joshua trees to survive climate change is protecting them from the direct impact of human activities.
Joshua trees are a part of the Agavaceae family and are also known by the name of Yucca brevifolia. It is a type of tree-like yucca that grows in arid regions such as the Mojave Desert. These trees are known for their unique, spiky green leaves and their rough trunk that has sharp leaves which grow upward. Joshua trees have a lifespan of about 500 to 1000 years and can grow up to 40 feet tall.
Joshua trees are being threatened due to climate change. Climate change is affecting their natural habitat and therefore, they cannot germinate and grow as easily as they used to do before. As a result, the number of Joshua trees is on the decline. To ensure the survival of these trees, we need to act immediately.
One of the most effective ways to help the Joshua trees survive climate change is to protect them from the direct impact of human activities. There are various ways to do this such as reducing carbon emissions, minimizing deforestation, promoting reforestation, and more. If we want these trees to survive, we need to act now to prevent further damage to their habitat. By protecting these trees from the negative effects of climate change, we can ensure their survival and preserve their beauty for generations to come.
To know more about Joshua trees: https://brainly.com/question/12682491
#SPJ11
which type of electromagnetic radiation has more energy than visible light and can pass through the human body?
X-rays have more energy than visible light and can pass through the human body.
X-rays are a type of electromagnetic radiation that has a shorter wavelength and higher frequency than visible light. Due to their high energy, X-rays can penetrate solid objects, including the human body. This property makes X-rays useful in medical imaging, such as X-ray radiography, computed tomography (CT) scans, and mammography.
When X-rays pass through the human body, they can be absorbed by the tissues or pass through, depending on the density of the material. Bones, for example, absorb more X-rays than soft tissues like muscle or fat, which is why they appear white in X-ray images.
While X-rays can be helpful in diagnosing medical conditions, they can also be harmful if exposure is not limited or controlled. Prolonged exposure to X-rays can damage DNA and potentially lead to cancer or other health problems.
For more similar questions on "soft tissues"
brainly.com/question/26135103
#SPJ11
The symbol EF represents the magnitude of the electric field at location F, and the symbol Ep represents the magnitude of the electric field at location D. Which of the following equations is a correct energy conservation (loop) equation for this circuit, following a path that starts at the positive end of the battery and goes clockwise? O o- 1.5 V- Ef 0.25 m ED 0.063 m - Ef 0.25 m 0+1.5 V- EF 0.25 m ED 0.063 m-Ef 0.25 m 1.5 V- EF .0.25 m 0+1.5EF 0.25 mED -0.063 mEf 0.25 m 0-1.5 VEf 0.25 m ED 0.063 mEf-0.25 m 1.5V- ED-0.063 m The symbol i represents the electron current at location F, etc. Which of the following equations is a correct charge conservation (node) equation for this circuit? Use the appropriate equation(s), plus the equation relating electron current to electric field, to solve for the factor that goes in the blank below: *ED Use the appropriate equation(s) to calculate the magnitude of ED ED Use the appropriate equation(s) to calculate the electron current at location D in the steady state: V/m
The correct energy conservation (loop) equation for this circuit is 1.5V - EF 0.25m + ED 0.063m - EF 0.25m + 1.5V - EF 0.25m + ED 0.063m - EF 0.25m + 1.5V - ED 0.063m = 0.
The correct charge conservation (node) equation is i + EF 0.25m - ED 0.063m = 0. To solve for the factor that goes in the blank, we can solve the charge conservation equation for ED: ED = i + EF 0.25m. Therefore, ED = V/m. To calculate the magnitude of ED, substitute the known values into the equation: ED = V/m = (1,5V + 0,25m . EF)/0,063m.
To calculate the electron current at location D in the steady state, substitute the known values into the charge conservation equation: i = ED - EF 0.25m = (V/m - 0.25m*EF).
Learn more about Energy conservation: brainly.com/question/31047668
#SPJ11
A sandbag is dropped from a balloon which is ascending vertically at a constant speed of 6 m/s.
If the bag is released with the same upward velocity of 6 m/s when t = 0 and hits the ground when t = 8 s, determine the speed of the bag as it hits the ground and the altitude of the balloon at this instant.
The speed of the bag as it hits the ground is -47.2 m/s and the altitude of the balloon at this instant is 245.6 m.
At t = 0, the sandbag is released with an upward velocity of 6 m/s. Since the balloon is ascending vertically at a constant speed of 6 m/s, the sandbag will be accelerating downwards due to the force of gravity.
Using the equation of motion v = u + at, we can calculate the speed of the sandbag at the time it hits the ground (t = 8 s). We can calculate the velocity by substituting u = 6 m/s, a = -9.8 m/s2 (acceleration due to gravity), and t = 8 s. This gives us a velocity of -47.2 m/s.
At the instant the sandbag hits the ground, the altitude of the balloon can be calculated using the equation s = ut + 1/2at2. We can calculate the altitude by substituting u = 6 m/s, a = -9.8 m/s2, and t = 8 s. This gives us an altitude of 245.6 m.
Therefore, the speed of the bag as it hits the ground is -47.2 m/s and the altitude of the balloon at this instant is 245.6 m.
To learn more about speed follow
https://brainly.com/question/14691279
#SPJ11
the amount of work (in j) an external agent must do to stretch the spring 7.40 cm from its unstretched position (in joule)
The external agent must do 0.037 J of work to stretch the spring 7.40 cm from its unstretched position.
To calculate the amount of work an external agent must do to stretch a spring 7.40 cm from its unstretched position, we need to use the formula:
[tex]W = (1/2) kx^2[/tex]
where:
W = work done by the external agent (in joules)
k = spring constant (in newtons/meter)
x = displacement from the unstretched position (in meters)
First, we need to convert the displacement from centimeters to meters:
x = 7.40 cm = 0.0740 m
Let us assume the spring constant is [tex]k[/tex].
Now, we can substitute the values into the formula:
[tex]W = (1/2) kx^2[/tex]
[tex]W = (1/2) (k \ N/m) (0.0740\ m)^2[/tex]
[tex]W = 0.037k \ J[/tex]
Hence work done by the external agent is [tex]0.037k\ J[/tex].
Learn more about spring:
https://brainly.com/question/14670501
#SPJ11
a neutral metal sphere is touched to a negatively charged metal rod. As a result the sphere will be_____ and the metal rod will be ________ . Fill in the gaps
a. positively charger. b.negatively charger. c. neutral. d. none
A neutral metal sphere is touched to a negatively charged metal rod. As a result the sphere will be a. positively charged and the metal rod will be b. negatively charged.
When a neutral metal sphere is touched to a negatively charged metal rod, the sphere will be positively charged, and the metal rod will be negatively charged. The process of charging through contact is known as contact electrification, triboelectrification, or electrostatic induction. It occurs when two different materials come into contact and exchange electrons, causing one of them to become positively charged and the other to become negatively charged.
As a result, a neutral metal sphere is touched to a negatively charged metal rod, the negatively charged rod donates some of its electrons to the sphere, giving it a net positive charge. The metal sphere will repel positively charged objects and attract negatively charged objects due to the positive charge it has acquired. The negatively charged rod will repel negatively charged objects and attract positively charged objects due to the negative charge it has acquired. Hence, the correct option is a. positively charged and b. negatively charged.
Learn more about triboelectrification at:
https://brainly.com/question/30543807
#SPJ11
two long parallel wires placed side-by-side on a horizontal table carry identical current straight toward you. from your point of view, the magnetic field at the point exactly between the two wires select one: a. points down. b. points toward you. c. is zero. d. points away from you.
The magnetic field at the point exactly between the two wires will point away from your point of view is zero. The correct option is C.
What is the magnetic field?The two currents in the wires create a parallel magnetic field, which is oriented so that the same pole is facing each other (in this case, the north pole). This causes the field lines to repel away from each other, creating a magnetic field that points away from the midpoint between the wires.
The magnetic field at the point exactly between the two wires is zero. Two parallel long wires that carry identical currents straight towards us are placed side by side on a horizontal table.
As a result, the net magnetic field is zero.
Therefore, the correct option is C.
Read more about magnetic field here:
https://brainly.com/question/14411049
#SPJ11
a microwave oven operates at 2.90 ghz . what is the wavelength of the radiation produced by this appliance?
The given frequency of a microwave oven is 2.90 GHz. We have to find the wavelength of the radiation produced by this appliance. The speed of light is a constant value of 3 x 108 m/s. The relation between frequency and wavelength of electromagnetic radiation is given by:
c = fλ
Where,
c = speed of lightf = frequency of radiationλ = wavelength of radiationWe can rearrange this equation to get the formula for wavelength:
λ = c / f
Substituting the given values, we get:
λ = 3 x 108 / (2.90 x 109)λ = 0.1034 m or 10.34 cmTherefore, the wavelength of the radiation produced by the microwave oven is 10.34 cm.
Learn more about microwave oven: https://brainly.com/question/3164926
#SPJ11
fifty points Hypothesis: Predict how the addition of subatomic particles will affect the structure and properties of an atom. (Example: I predict that adding more neutrons will affect . . .)
Was your hypothesis correct? Why or why not?
Website: https://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html
Open the Phet build-an-atom simulator.
Answer:
Hypothesis: Adding subatomic particles to an atom will affect its structure and properties. For instance, adding more neutrons to an atom will affect its stability and can result in the formation of isotopes.
The hypothesis is correct. Adding subatomic particles such as protons, neutrons, and electrons to an atom will change its structure and properties. The number of protons determines the atomic number and the identity of the element. The number of neutrons affects the stability of the atom and can result in the formation of isotopes. Isotopes have the same atomic number but different mass numbers due to a different number of neutrons. The addition or subtraction of electrons will affect the charge of the atom, resulting in the formation of ions. Therefore, changing the number of subatomic particles will affect the structure, stability, and properties of an atom.
Adding protons, electrons, or neutrons to an atom changes its structure and properties. Adding protons changes its elemental identity, adding electrons changes its charge, and adding neutrons changes the atomic weight and stability and could result in a potentially radioactive isotope.
Explanation:Adding subatomic particles to an atom can have significant impacts on its structure and properties. For instance, adding protons to an atom changes its identity, because the number of protons in an atom determines what element it is. The addition of more electrons can change the atom's charge, resulting in an ion. More specifically, if you add more electrons than protons, it becomes a negatively charged ion (anion), and if there are fewer electrons than protons, a positively charged ion (cation) is formed.
Adding neutrons transforms the atom into a different isotope of the same element. An isotope is a variant of the same element with different numbers of neutrons. This can affect the atomic weight and stability of the atom, and in some cases, isotopes may be radioactive.
Learn more about subatomic particles here:https://brainly.com/question/32192242
#SPJ2
the fact that we observe neutrinos from the sun provides direct evidence of the fact that we observe neutrinos from the sun provides direct evidence of the existence of the solar wind. fusion in the sun's core. convection in the sun's interior.
The fact that we observe neutrinos from the sun provides direct evidence of the fact that we observe neutrinos from the sun provides direct evidence of fusion in the sun's core. This is because neutrinos are created as a result of nuclear fusion processes occurring within the sun's core.
Neutrinos are subatomic particles that are created in the nuclear reactions that occur within the sun's core. They are tiny, lightweight, and lack an electric charge. As a result, they can travel through matter, including the sun's interior, with relative ease without being deflected or absorbed. Fusion refers to the process of combining two atomic nuclei together to form a new nucleus. This process releases a tremendous amount of energy and is the driving force behind the sun's heat and light.
The sun fuses hydrogen nuclei into helium nuclei in its core, which releases energy in the form of light and heat. This process generates a tremendous amount of neutrinos, which stream out from the sun in all directions. The solar wind refers to a stream of charged particles, mostly protons and electrons, that are emitted by the sun's corona, it travels outwards through the solar system and can interact with the Earth's magnetic field, producing auroras and other phenomena. While neutrinos are not directly related to the solar wind, they are produced as a result of the same nuclear fusion processes that occur in the sun's core.
Learn more about solar wind at:
https://brainly.com/question/28227208
#SPJ11
a piston cylinder containing air has an area of 0.011 m2 and a piston with a mass of 20.4 kg. if the atmospheric pressure is measured to be 102.3 kpa, what is the gauge pressure of the air inside the piston cylinder? the absolute pressure?
The gauge pressure of the air inside the piston cylinder is 21.849 kPa if the atmospheric pressure is measured to be 102.3 kpa .
What is gauge pressure ?The pressure relative to atmospheric pressure is known as gauge pressure. Gauge pressure is positive for pressures greater than atmospheric pressure and negative for pressures less than atmospheric pressure. In fact, atmospheric pressure increases the pressure in any fluid that is not contained in a rigid container. This occurs as a result of Pascal's principle.
Absolute pressure on piston = atmospheric pressure + pressure on piston
solving , 102.3 kPa
to know more about gauge pressure , visit ;
brainly.com/question/29341536
#SPJ1
The gauge pressure of the piston cylinder will be 17889.5 KPa and the absolute pressure of the piston cylinder will be 17991.8 KPa.
What is the gauge pressure?The gauge pressure inside the piston cylinder is calculated by subtracting the atmospheric pressure from the total pressure inside the cylinder. Therefore, the gauge pressure of the air inside the piston cylinder is calculated as follows:
Pgauge = Ptotal - Patm
Pgauge = F/A - Patm
Pgauge = (20.4kg × 9.8m/s²) / 0.011m² - 102.3 kPa
Pgauge = 17991.8 kPa - 102.3 kPa
Pgauge = 17889.5 kPa
The absolute pressure inside the piston cylinder is the sum of the atmospheric pressure and the gauge pressure. Therefore, the absolute pressure of the air inside the piston cylinder is calculated as follows:
Pabsolute = Pgauge + Patm
Pabsolute = 17889.5 kPa + 102.3 kPa
Pabsolute = 17991.8 kPa
Learn more about Pressure here:
https://brainly.com/question/29341536
#SPJ11
which of the following includes all common types of radioactive decay? a. atomic number, beta particle emission, electron capture B. alpha particle emission, beta particle emission, half-life C. alpha particle emission, beta particle emission, radioactive parent isotope D. alpha particle emission, beta particle emission, electron capture E. alpha particle emission, stable daughter, electron capture
Alpha particle emission, beta particle emission, and electron capture are all common types of radioactive decay.The correct answer is D.
They are common types of radioactive decay's because:
Alpha particle emission involves the emission of an alpha particle (a helium nucleus) from the nucleus of an atom. This reduces the atomic number by 2 and the mass number by 4.Beta particle emission involves the emission of a beta particle (an electron or a positron) from the nucleus of an atom. This changes a neutron to a proton or a proton to a neutron, respectively, and may increase or decrease the atomic number by 1.Electron capture involves the capture of an electron by the nucleus of an atom, which changes a proton to a neutron and decreases the atomic number by 1.Option D includes all of these types of radioactive decay (alpha particle emission, beta particle emission, and electron capture), so it is the correct answer
To learn more about radioactive decay:
https://brainly.com/question/11117468
#SPJ11
A basketball rolls across a floor without slipping, with its centerof mass moving at a certain velocity. A block of ice of the samemass is set sliding across the floor with the same speed along aparallel line.(a) How do their energies compare?The ice has more kineticenergy.They have equal kineticenergies.The basketball has more kineticenergy.
The correct option is A, A block of ice of the same mass is set sliding across the floor with the same speed along a parallel line The ice has more kinetic energy.
Kinetic energy is a type of energy that an object possesses by virtue of its motion. It is defined as the energy an object has due to its motion and is proportional to the mass of the object and the square of its velocity. The formula for kinetic energy is KE = 1/2mv², where m is the mass of the object and v is its velocity.
Kinetic energy is a scalar quantity and has units of joules in the International System of Units (SI). It is a fundamental concept in physics and is used to describe many physical phenomena, including the motion of particles, the behavior of gases, and the motion of waves. In many cases, kinetic energy can be transformed into other forms of energy. For example, when a ball is thrown upwards, its kinetic energy is gradually converted into gravitational potential energy as it moves higher and higher.
To learn more about Kinetic energy visit here:
brainly.com/question/26472013
#SPJ4
Complete Question:
Basketball rolls across a floor without slipping, with its center of mass moving at a certain velocity. A block of ice of the same mass is set sliding across the floor with the same speed along a parallel line.(a) How do their energies compare?
A). The ice has more kinetic energy.
B). They have equal kinetic energies.
C). The basketball has more kinetic energy.
The steel shaft has a diameter of 2 in. It is supported on smooth journal bearings A and B, which exert only vertical reactions on the shaft. Determine the absolute maximum bending stress in the shaft if it is subjected to the pulley loadings shown.
The absolute maximum bending stress in the shaft if it is subjected to the pulley loadings is (P1 + P2 + RA + RB) / (π x (2)^2/4).
The maximum bending stress in a steel shaft with a diameter of 2 in, subjected to pulley loadings, can be determined using the following equation:
σ = P/(π x d^2/4)
where P is the load in pounds, and d is the diameter of the shaft in inches.
In this case, P is the sum of the two pulley loads. Since the bearings A and B are only exerting vertical reactions on the shaft, these should be included in the calculation.
Therefore, the maximum bending stress in the steel shaft is σ = (P1 + P2 + RA + RB) / (π x (2)^2/4). This value should be compared to the allowable bending stress for the material to ensure that the shaft is designed to handle the applied loads without exceeding the material's strength properties.
For more such questions on Bending stress.
https://brainly.com/question/13001989#
#SPJ11
Suppose we can model a certain cyanine-type dye molecule as having 10 electrons confined to a one-dimensional box of length L. Imagine that we use an external source of light to illuminate a sample of this molecule with photons having just the right energy to excite electrons from the n= 5 level to the n=7 level of the box. (a) When such excited electrons decay back toward their lowest available energy state, in addition to reradiating photons of the same energy as those from the external source, they can radiate photons of two and only two other longer wavelengths (this is the phenomenon known as fluorescence). Using an energy-level diagram showing possible transitions, identify the two transitions that produce these photons and explain why others (say, from the n=7 to the n=1 level) are impossible.(b) Assume that, of the photons discussed in part (a), the ones with the longest wavelength have a wavelength of 600 nm (in the red-orange region of the spectrum). What is the wavelength of the original photons from the external source? Are the photons from the external source visible?
(a) The two transitions that produce photons of longer wavelengths during fluorescence are from n=7 to n=5 and from n=6 to n=5.
These transitions are allowed because the energy difference between the n=7 and n=5 levels and between the n=6 and n=5 levels is equal to the energy of a photon with a longer wavelength than the excitation wavelength.
Transitions from n=7 to n=1 or from n=6 to n=1, for example, are not possible because the energy difference between these levels is greater than the energy of the excitation photon. Therefore, the excited electrons cannot decay to these lower energy levels by emitting a photon of lower energy than the excitation photon.
(b) The energy difference between the n=7 and n=5 levels is the same as the energy difference between the n=6 and n=5 levels. Therefore, the wavelength of the photon emitted during the n=7 to n=5 transition is the same as the wavelength of the photon emitted during the n=6 to n=5 transition.
If the longest wavelength of the fluorescence photons is 600 nm, we can use the following equation to calculate the energy of a photon with this wavelength:
E = hc/λ
where h is Planck's constant, c is the speed of light, and λ is the wavelength in meters.
Converting the wavelength to meters, we get:
λ = 600 nm = [tex]6.0 \times 10^{-7} m[/tex]
Substituting into the equation and solving for E, we get:
E = [tex](6.626 \times 10^{-34} Js)(3.00 \times 10^8 m/s)/(6.0 x 10^{-7} m) = 3.31 x 10^-19 J[/tex]
Since the energy of the excitation photon is equal to the energy difference between the n=5 and n=7 levels, we can use the following equation to calculate the wavelength of the excitation photon:
[tex]\Delta E = E_{n7} - E_{n5} = (h^2/8mL^2)(49-25) = 24h^2/(8mL^2)[/tex]
E_photon = hν = ΔE
ν = ΔE/h
λ = c/ν = hc/ΔE
Substituting the values, we get:
[tex]\lambda = hc/(24h^2/(8mL^2)) = 8mL^2c/3h[/tex]
Hence the wavelength of the original photon is [tex]8mL^2c/3h[/tex].
Learn more about fluorescence:
https://brainly.com/question/24228588
#SPJ11
a thin spherical metallic shell of radius 2.31 cm is has a charge of -3.1 uc uniformly distributed on its surface. what direction does the electric field point at a distance of 4.2 cm from the origin? a. there is no electric field b. radially outward c. tangential to the surface d. radially inward
The electric field's direction is radially inward because the charge is negative. Hence, the correct option is (d)
The given electric charge is -3.1uc, uniformly distributed over a thin spherical metallic shell with a radius of 2.31cm.
The electric field direction at a distance of 4.2cm from the origin can be found using Gauss's law.
The electric field is proportional to the electric charge enclosed by the spherical metallic shell within a closed surface.
The electric flux is defined as the electric field passing through the closed surface divided by the electric field.
For instance, The electric flux through a closed surface is proportional to the electric charge enclosed by that surface.
E is the electric field,
ΦE is the electric flux, and
Qenc is the electric charge enclosed by the surface in Gauss's law.
Here, the Gaussian surface is a sphere with a radius of 4.2cm.
We can calculate the electric field direction using the same formula as before, which is given by;
E = Qenc/4πε0r², where r = 4.2cm
Let's substitute the values and simplify = (-3.1 x 10⁻⁶)/(4π x 8.85 x 10⁻¹² x (4.2 x 10⁻²)²)E = -5.82 x 10⁴ N/C
Therefore, radially inward. The electric field is a vector field that exists around charged objects.
The field is proportional to the charge and inversely proportional to the distance between the charges.
A positive charge will emit electric field lines, whereas a negative charge will attract them. The electric field is represented by the letter E and is calculated in units of newtons per coulomb (N/C).
To learn more about the electric field:https://brainly.com/question/19878202
#SPJ11
Complete the following ---
Area of piston A: 0.01m^2
Force applied on piston A: 6N
Pressure in the liquid: ?
Area of piston B: 0.1cm^2
Force produced by piston B: ?
(note: there's a difference of m^2 and cm^2 in the areas so it's difficult for me...)
Answer: The force produced by piston B is 0.006 N.
Explanation:
No problem! We can convert the area of piston B to square meters to make the units consistent:
Area of piston B = 0.1 cm^2 = 0.1 x (0.01 m/cm)^2 = 0.00001 m^2
Now we can use the formula:
pressure = force/area
For piston A, we have:
pressure = 6 N / 0.01 m^2 = 600 Pa
So the pressure in the liquid is 600 Pa.
To find the force produced by piston B, we rearrange the formula:
force = pressure x area
Using the pressure we just found and the area of piston B, we get:
force = 600 Pa x 0.00001 m^2 = 0.006 N
So the force produced by piston B is 0.006 N.
Which statement describes what most likely occurs when a magnetic compass is placed next to a simple circuit made from a battery, a light bulb, and a wire?A magnetic field created by the compass causes the light bulb to stop working.A magnetic field created by the electric current causes the compass needle to move.A magnetic field created by the compass increases the current in the electrical circuit.A magnetic field created by the electric current places negative charges on the compass.
A magnetic field created by the electric current causes the compass needle to move. This is the most likely outcome when a magnetic compass is placed adjacent to a basic electrical circuit consisting of a battery, a light bulb, and a wire.
A magnetic field is created around a wire as electricity flows through it. The compass needle moves as a result of the interaction between this magnetic field and the Earth's magnetic field. Consequently, the magnetic field produced by the electric current in the wire causes the compass needle to move when a magnetic compass is put next to a basic circuit comprised of a battery, a light bulb, and a wire. The interplay of magnetic fields and electric currents is employed in numerous applications, such as electric motors and generators, to transform electrical energy into mechanical energy and vice versa.
learn more about magnetic compass here:
https://brainly.com/question/2264542
#SPJ4
the us bank tower in los angeles is designed to resist an earthquake of what magnitude on the richter scale?
The 8.3 on the Richter scale earthquake magnitude can be withstood by the US Bank Tower in Los Angeles.
How earthquake-proof is the Los Angeles U.S. Bank Tower?A frame that is strengthened in two directions is part of the central core structure. Two struts, each one level high, are employed to decrease horizontal stresses brought on by wind or earthquakes beginning at the 53rd floor.
A 9.0 earthquake can a tower withstand?Indeed, it is the answer. Modern structural design techniques can be used to construct skyscrapers that can resist earthquakes. Performance-based structural design (PBSD), a cutting-edge design methodology for creating earthquake-resistant structures, is one of them.
To know more about magnitude visit:-
https://brainly.com/question/30395926
#SPJ1
Lab: Electromagnetic Induction: Instructions Click the links to open the resources below. These resources will help you complete the assignment. Once you have created your file(s) and are ready to upload your assignment, click the Add Files button below and select each file from your desktop or network folder. Upload each file separately. Your work will not be submitted to your teacher until you click Submit.
To complete the lab assignment on Electromagnetic Induction, first click the links to open the resources provided.
This will help you complete the task.
After creating the file(s) and once you are ready to submit your assignment,
click the 'Add Files' button and select each file from your desktop or network folder.
Remember to upload each file separately. Once you have uploaded the files, click 'Submit' to submit your work to your teacher.
In this lab, you are expected to understand and apply the concept of Electromagnetic Induction.
Electromagnetic Induction is a process where a varying magnetic field creates an electric field.
The electric field then induces a current in a nearby circuit. This current is caused by Faraday's law of induction.
To know more about Electromagnertic induction; https://brainly.com/question/27613726
#SPJ11
Is it possible to have an acceleration without having a force?
No, there must always be a force present in order to have an acceleration. This is because, according to Newton's Second Law of Motion, acceleration is exactly proportional to force.
An item will accelerate more quickly the more force is given to it. An object's velocity will remain constant without a force acting on it (whether it is at rest or moving with a constant speed and direction), hence its acceleration will be zero. One of Newton's Three Laws of Motion, this is referred to as the Law of Inertia. No, an acceleration always requires the presence of a force. This is because acceleration is eminently proportional to force, in accordance with Newton's Second Law of Motion. it NOT possible to have an acceleration without having a force.
learn more about force here:
https://brainly.com/question/13191643
#SPJ4
what does it mean when a metamorphic rock has foliation?
Answer:
The rock has been layered.
Explanation:
Foliation is the repeated layering of rock. It usually happens when there's extensive heat or pressure in one direction.
find the energy (in terms of kt) above the fermi level, for which the fermi-dirac probability is within 1% of the boltzmann approximation.
The energy above the Fermi level, in terms of kT, for which the Fermi-Dirac probability is within 1% of the Boltzmann approximation is kT/2.
This is because the Boltzmann approximation is valid for energies much larger than the Fermi energy, so in this case the energy is kT/2, where k is the Boltzmann constant and T is the temperature. The Fermi-Dirac probability is then within 1% of the Boltzmann approximation.
Learn more about fermi level at: brainly.com/question/19091696
#SPJ11
To go from a lower level in an atom to a higher level, an electron must give off a photon of energy lose its electric charge absorb a photon of energy wait until the atom has changed into another atom with more protons get a permission slip from Niels Bohr
An electron must absorb a photon of energy in order to go up an atom's levels. The electron gains energy as a result and jumps to a higher energy level.
An electron in an atom must absorb a photon of energy equal to the energy difference between the two levels in order to go from one level of energy to another. Excitation is the term for this action. The electron is elevated to a higher energy level after absorbing the photon. The electron will swiftly revert to its initial energy level, producing a photon with an energy equal to the difference between the two levels, as this is an unstable condition. A photon is released as a result of this procedure, which is also known as de-excitation or relaxation. Instruments that can detect this photon can be used to examine the energy levels of atoms.
learn more about electron here:
https://brainly.com/question/1255220
#SPJ4
One of the stable isotopes of lithium has 3 protons and 4 neutrons, so its atomic mass is 7. Assume that a lithium atom initially at rest radiates a photon of energy 1.8488 eV and recoils.
How long does it take for the recoiling atom to travel 1 mm? Assume that the lithium atom travels in a straight line without any collisions.
Note: 1 amu = 1.66 × 10-27 kg
t =
It takes 1.196 × 10-8 seconds for the recoiling lithium atom to travel 1mm.
We know that the energy of the photon is E = 1.8488 eV. The momentum of the photon is given by:
p = E/c
where c is the speed of light.
Substituting the values we get:
p = 1.8488 × 1.6 × 10-19/3 × 108p = 6.160 × 10-28 kg m/s
By the conservation of momentum, the momentum of the lithium atom will be equal in magnitude and opposite in direction to the photon. Therefore, we can write:
|p atom| = |p photon|
p atom = 6.160 × 10-28 kg m/s
Let m be the mass of the lithium atom. We can now use the kinetic energy equation:
KE = 1/2mv^2
where KE is the kinetic energy of the atom, and v is the velocity of the atom. Initially, the atom is at rest. After the photon is emitted, the atom recoils with velocity v. Therefore, we can write:
KE = E
kinetic energy of the atom = E = 1.8488 e
V = 1.8488 × 1.6 × 10-19 Joules
v = √2E/m
where m is the mass of the lithium atom.
Substituting the value of m, we get:
v = √2 × 1.8488 × 1.6 × 10-19/6.941 × 10-26v = 8.373 × 105 m/s
Time taken to travel 1 mm is given by
t = distance/velocity
where the distance is 1 mm = 1 × 10-3 m.
Substituting the values, we get:
t = 1 × 10-3/8.373 × 105
t = 1.196 × 10-8 seconds.
Learn more about Lithium:
https://brainly.com/question/28449914
#SPJ11
The standard free energy for the reaction of oxygen binding to myoglobin Mb+O2(g)⇌ MbO2 is ΔG∘=−30.0kJmol−1 at 298 K and pH=7. The standard state of O2 is the dilute solution, molarity scale; therefore the concentration of O2 must be in M. What is the ratio MbO2/Mb in an aqueous solution at equilibrium with a partial pressure of oxygen pO2=400 Pa? Assume ideal behavior of O2 gas and for the protein in solution.
The ratio of MbO₂ to Mb at equilibrium with a partial pressure of oxygen pO₂ is 0.00002.
The ratio of MbO₂ to Mb in an aqueous solution at equilibrium with a partial pressure of oxygen pO₂ = 400 Pa can be calculated using the equation ΔG∘=−30.0 kJmol−1 at 298 K and pH = 7.
The equation used is: ΔG∘ = -RT ln (MbO₂/Mb), where R is the ideal gas constant and T is temperature in Kelvin. Rearranging this equation gives MbO₂/Mb = e^(-ΔG∘/RT).
Therefore, the ratio of MbO₂ to Mb at equilibrium with a partial pressure of oxygen pO₂ = 400 Pa is e^(-30.0/8.314*298) = 0.00002.
learn more about oxygen and solution at : https://brainly.com/question/1245440
#SPJ11
