(a) The de Broglie wavelength is approximately 5.175 × 10⁻¹⁵ meters. The wavelength is lesser than the distance of closest approach
(b) It is proper to treat the alpha particle as a particle and not as wave because the distance of closest approach is much larger than and not comparable to its wavelength for the alpha particle for the alpha particle to be treated as a wave
The given parameters are;
The kinetic energy of the alpha particles = 7.70 MeV = 1.23368 × 10⁻¹² J
The distance from the gold nucleus the alpha particles reach = 29.5 fm
(a) The de Broglie wavelength of a particle is given as follows;
[tex]\mathbf{\lambda = \dfrac{h}{p}}[/tex]
Where;
λ = The wavelength
h = Planck's constant = 6.62607004 × 10⁻³⁴ m²·kg/s
p = The momentum of the particle = Mass of an electron, m × Velocity, v
The mass of an alpha particle, m ≈ 6.645 × 10⁻²⁷ kg
Therefore;
[tex]\lambda = \dfrac{h}{m \times v}[/tex]
The kinetic energy of the alpha particle, K.E. = (1/2)·m·v²
∴ v = √(2 × K.E./m)
Therefore;
[tex]\lambda = \dfrac{h}{m \times \sqrt{2 \times \dfrac{K.E.}{m} } } = \dfrac{h}{ \sqrt{2 \times m \times K.E.} }[/tex]
Plugging in the values of the variables gives;
[tex]\lambda = \dfrac{6.62607004 \times 10 ^{-34} }{ \sqrt{2 \times 6.645 \times 10 ^{-27} \times 1.23368 \times 10^{-12} } } \approx 5.175 \times 10^{-15}[/tex]
The de Broglie wavelength of the alpha particle, λ ≈ 5.175 × 10⁻¹⁵ m
The distance of closest approach = 29.5 fm = 29.5 × 10⁻¹⁵ m
Compared to the distance of closest approach, the wavelength of the alpha particle is lesser than the distance of closest approach
(b) Given that the distance of closest approach is six times larger than the wavelength of the alpha particle, and alpha particle behaving as waves are expected to approach closer to the gold nucleus in the region of their wavelength before deflection, therefore, the larger distance of closest approach is indicative of a charged particle to charged particle interaction, and therefore, particle behavior of alpha particles.
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what is the source of energy
which best describes how air moves during convection?
a. cool air warms as it mixes with denser air
b. warm air cools as it mixes with cooler, denser air
c. warm air is displaced by cooler denser air
a. cool air warms as it mixes with denser air
Explanation:
c. warm air is displaced by cooler denser air
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Which statement explains how constructive interference supports the wave model of light rather than the particle model?
O A. Light strikes a metal surface and knocks electrons loose, which particles would not do.
O B. Two light beams intersect, joining together to form a brighter beam, which is a behavior of waves.
O C. Two beams of light intersect, canceling each other out and forming a weaker beam, which is a behavior of waves.
O D. Light waves bend around a corner, but particles would not travel in bent paths.
Answer:
B. Two light beams intersect, joining together to form a brighter beam, which is a behavior of waves
Explanation:
Constructive interference of waves is the effect of the combination of two waves by the addition of their maxima and minima to produce a wave that has an amplitude which is the combination or the sum of the amplitudes of the two initially separate waves
Therefore, the statement, two light beams intersect, joining together to form a brighter beam, which is explainable by the constructive interference of waves, which is a wave behavior, supports the wave model of light rather than the particle model.
Which statements describe a situation with a displacement of zero? Check all that apply.traveling south for 30 miles, then turning west and traveling another 30 milesriding on a Ferris wheel whose entrance and exit are the samewalking around the block, starting from and ending at the same houseriding on an escalator from the bottom floor to the top floorrunning exactly one lap around a racetrack
Answer:
• riding on a Ferris wheel whose entrance and exit are the same
• walking around the block, starting from and ending at the same house
• running exactly one lap around a racetrack
Explanation:
Displacement simply means the.change in position of an object. In a situation whereby the initial and final position are thesame, the displacement will be zero.
The statements that describe a situation with a displacement of zero include:
• riding on a Ferris wheel whose entrance and exit are the same
• walking around the block, starting from and ending at the same house
• running exactly one lap around a racetrack
Answer:
• riding on a Ferris wheel whose entrance and exit are the same
• walking around the block, starting from and ending at the same house
• running exactly one lap around a racetrack
Explanation:
B,C,E
The engine starter and a headlight of a car are connected in parallel to the 12.0-V car battery. In this situation, the headlight operates at 38 W and the engine starter operates at 2.40 kW. If the headlight and starter were then rewired to be in series with each other, what total power would they consume when connected to the 12.0-V battery
Answer:
The total power they will consume in series is approximately 2.257 W
Explanation:
The connection arrangement of the headlight and the engine starter = Parallel to the battery
The voltage of the battery, V = 12.0 V
The power at which the headlight operates in parallel, [tex]P_{headlight}[/tex] = 38 W
The power at which the kick starter operates in parallel, [tex]P_{kick \ starter}[/tex] = 2.40 kW
We have;
P = V²/R
Where;
R = The resistance
V = The voltage = 12 V (The voltage is the same in parallel circuit)
For the headlight, we have;
R₁ = V²/[tex]P_{headlight}[/tex] = 12²/38 = 72/19
R₁ = 72/19 Ω
For the kick starter, we have;
R₂ = V²/[tex]P_{kick \ starter}[/tex] = 12²/2.4 = 60
R₂ = 60 Ω
When the headlight and kick starter are rewired to be in series, we have;
Total resistance, R = R₁ + R₂
Therefore;
R = ((72/19) + 60) Ω = (1212/19) Ω
The current flowing, I = V/R
∴ I = 12 V/(1212/19) Ω = (19/101) A
We note that power, P = I²R
In the series connection, we have;
[tex]P_{headlight}[/tex] = I² × R₁
∴ [tex]P_{headlight}[/tex] = ((19/101) A)² × 72/19 Ω = 1368/10201 W ≈ 0.134 W
The power at which the headlight operates in series, [tex]P_{headlight, S}[/tex] ≈ 0.134 W
[tex]P_{kick \ starter}[/tex] = ((19/101) A)² × 60 Ω = 21660/10201 W ≈ 2.123 W
The power at which the kick starter operates in series, [tex]P_{kick \ starter, S}[/tex] ≈ 2.123 W
The total power they will consume, [tex]P_{Total}[/tex] = [tex]P_{headlight, S}[/tex] + [tex]P_{kick \ starter, S}[/tex]
Therefore;
[tex]P_{Total}[/tex] ≈ 0.134 W + 2.123 W = 2.257 W
An object elongates from a length of 45 cm to a length of 55 cm. The percent strain is
41%
22%
122%
82%
18%
36%
Answer:
22%
Explanation:
55 - 45 = 10
10/45 simplifies to 2/9
2/9 = 0.22222... so 22.22% (rounded 22%)
Match each feature related to the process of seafloor spreading with its location on the diagram
Answer:
Seafloor spreading is a geological process that occurs in the ocean. It is occurs due to divergent plate tectonics. As, lithospheric plates of the ocean moves away from each other, the heat from the mantle liberates as convection currents that decreases the density of the crust. The less dense material rises, resulting the elevation of the seafloor, which is called as sea floor spreading.
Explanation:
slader At a carnival, you can try to ring a bell by striking a target with a 10.8-kg hammer. In response, a 0.408-kg metal piece is sent upward toward the bell, which is 4.23 m above. Suppose that 18.8 percent of the hammer's kinetic energy is used to do the work of sending the metal piece upward. How fast must the hammer be moving when it strikes the target so that the bell just barely rings
Answer:
The hammer must be moving at a speed of approximately 4.082 meters per second.
Explanation:
According to the statement and based on Principle of Energy Conservation, change in gravitational potential energy experimented by the metal piece ([tex]U_{g,o}[/tex]), in joules, must be equal to 18.8 percent of the translational kinetic energy of the hammer ([tex]K_{h}[/tex]), in joules.
[tex]U_{g, o} = 0.188\cdot K_{h}[/tex] (1)
By definitions of gravitational potential and translational kinetic energies, we expand (1):
[tex]m_{o}\cdot g\cdot h = 0.188\cdot \left(\frac{1}{2}\cdot m_{h}\cdot v^{2}\right)[/tex] (2)
Where:
[tex]m_{o}[/tex] - Mass of the metal piece, in kilograms.
[tex]g[/tex] - Gravitational acceleration, in meters per square second.
[tex]h[/tex] - Distance travelled by the metal piece, in meters.
[tex]m_{h}[/tex] - Mass of the hammer, in kilograms.
[tex]v[/tex] - Initial speed of the hammer, in meters per second.
If we know that [tex]m_{o} = 0.408\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], [tex]h = 4.23\,m[/tex] and [tex]m_{h} = 10.8\,kg[/tex], then the initial speed of the hammer is:
[tex]m_{o}\cdot g\cdot h = 0.188\cdot \left(\frac{1}{2}\cdot m_{h}\cdot v^{2}\right)[/tex]
[tex]10.638\cdot m_{o}\cdot g \cdot h = m_{h}\cdot v^{2}[/tex]
[tex]v = 3.261\cdot \sqrt{\frac {m_{o}\cdot g \cdot h}{m_{h}}}[/tex]
[tex]v = 3.261\cdot \sqrt{\frac{(0.408\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (4.23\,m)}{10.8\,kg} }[/tex]
[tex]v \approx 4.082\,\frac{m}{s}[/tex]
The hammer must be moving at a speed of approximately 4.082 meters per second.
A ball is launched horizontally at 150 m/s from a cliff. What is its vertical speed after 3 seconds?
A. 150 m/s
B. 50 m/s
C. 0 m/s
D. 30 m/s
Answer:
v_f = 30 m/s
Explanation:
v_f = v_I + a*t
v_f = 0m/s + (9.81m/s²)*(3s)
v_f = 29.43m/s
v_f = 30 m/s
Since the object is being launched horizontally off the cliff the only vertical force acting on the ball is gravity which is an acceleration of 9.81m/s². So we have all the flowing information to use the the kinematic equation: v_f = v_I + a*t.
Which wave has the smallest amplitude?
Answer:
C. C
Explanation:
A wave can be defined as a disturbance in a medium that progressively transports energy from a source location to another location without the transportation of matter.
In Science, there are two (2) types of wave and these include;
I. Electromagnetic waves: it doesn't require a medium for its propagation and as such can travel through an empty space or vacuum. An example of an electromagnetic wave is light.
II. Mechanical waves: it requires a medium for its propagation and as such can't travel through an empty space or vacuum. An example of a mechanical wave is sound.
A crest can be defined as the highest (vertically) point on a waveform.
On a related note, a trough is the lowest (vertically) on a waveform.
An amplitude can be defined as a waveform that's measured from the center line (its origin or equilibrium position) to the bottom of a trough or top of a crest. Thus, the vertical axis (y-axis) is the amplitude of a waveform i.e it's measured vertically.
In this scenario, waveform C which is represented by a blue curvy line has the smallest amplitude in comparison with the other waveforms because it has the minimum height when measured from the origin.
In contrast, waveform A represented by a purple line has the highest amplitude because it has the maximum height when measured from the origin.
Mathematically, the amplitude of a wave is given by the formula;
x = Asin(ωt + ϕ)
Where;
x is displacement of the wave measured in meters.A is the amplitude.ω is the angular frequency measured in rad/s.t is the time period measured in seconds.ϕ is the phase angle.Answer:
The answer is indeed D as the comment above suggests.
Explanation:
Simply put, wave D's highest point is closer to the line than all of the other high points of A, B and C
Help me please!!!!!!!!!
Answer:
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var running = null; console.log("Program Loading...");
var iframe = document.getElementById("stageFrame");
for (i = 0; i < 1; i++) {
setInterval(function() {
if (running == null) { running = true; console.log('Program Loaded! Enjoy!') }
if (iframe.contentWindow.document.getElementsByClassName('FrameRight') != null) { iframe.contentWindow.document.getElementsByClassName('FrameRight')[0].onclick(); }
if (iframe.contentWindow.document.getElementById("invis-o-div") != null) { iframe.contentWindow.document.getElementById("invis-o-div").remove(); }
},1000);
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Explanation:
Convertir 25 km/h a m/s
Answer:
6.9 m/s
Explanation:
1000m = 1km
3600s = 1hr
25000m/3600s
6.9m/s
While standing at a crosswalk, you hear a frequency of 510 Hz from an approaching police car.
After the police car passes, its frequency is 460Hz. What is the speed of the police car? (speed of
sound = 340 m/s)
Answer:
v = 17.68 m/s
Explanation:
Given that,
While standing at a crosswalk, you hear a frequency of 510 Hz from an approaching police car.
After the police car passes, its frequency is 460Hz.
We need to find the speed of the police car.
The formula is as follows :
[tex]v=\dfrac{v_o(f-f')}{f+f'}[/tex]
Put all the values,
[tex]v=\dfrac{343(510-460)}{510+460}\\\\=17.68\ m/s[/tex]
So, the speed of the police car is 17.68 m/s.
Cuánto demorará un cuerpo en alcanzar su máxima altura, sabiendo que fue lanzado, verticalmente hacia arriba, con una velocidad cuyo valor fue de 90 m/s?
Answer:
The maximum height reached is 413.27 m.
Explanation:
How long will it take for a body to reach its maximum height, knowing that it was thrown, vertically upwards, with a velocity whose value was 90 m / s?
initial velocity , u = 90 m/s
gravity, g = 9.8 m/s^2
Let the maximum height is h.
At maximum height the velocity v = 0
Use third equation of motion
[tex]v^2 = u^2 - 2 gh\\\\0 = 90\times 90 - 2 \times 9.8 \times h\\\\h = 413.27 m[/tex]
A frictionless pulley used to lift 8000N of concrete. What is the minimum effort required to raise the block
Answer: 8000N
Explanation: since it is frictionless that means it has 100% efficiency therefore the mechanical advantage is 1 meaning the load equals to the effort
Why is a flower not a good blackbody radiator?
Answer:
A flower emits only visible light
A flower reflects much of the light that hits it
Answer pls. This is for People like me with this Question . Help!!! Question 3 of 20 What happens to the electric force between two particles if the distance between them is reduced by half? O A. It decreases to half the original force. OB. It increases to twice the original force. O C. It increases to 4 times the original force. O D. It decreases to 1/4 of the original force.
Answer:
It increases twice the original
Size of image is equal to size of object in convex lens, when object is placed:
(a) at F
(b) between F & O
(c) between F & 2F
(d) at 2F
Pls answer fast
Explanation:
the object should be placed at 2F
Answer:
at 2F
Explanation:
hope it will help you
1. Which pair of physical quantities consists of two vectors?
a. Electric charge and momentum
b. Displacement and distance
c. Velocity and force
d. Temperature and kinetic energy
Answer:
Velocity and force consists of two vectors as they both have magnitude and direction
Pair of physical quantities consists of two vectors are velocity and force.
What are physical quantities ?"The seven elemental physical quantities are mass, time, temperature, mole, length, luminosity, and electrical charge. "Some derived physical quantities are velocity, heat, density, pressure, and momentum. Extensive physical quantities depend on the amount of substance or the size of the object.
What is velocity ?"Velocity is the speed at which something moves in a particular direction. For example as the speed of a car travelling north on a highway, or the speed a rocket travels after launching. "The scalar means the absolute value magnitude of the velocity vector is always be the speed of the motion.
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Is a nanoliter greater then one liter?
Different nutrients play different roles in our bodies. Which is the energy-storing nutrient?
O carbohydrates
O minerals
O proteins
O fats
Answer:
D. Fats
Explanation:
they are the long term energy storing nutrient carbohydrates are a quick way for energy minerals dont contain any energy and neither do proteins
fats
Explanation:
it is nutrient kept in the body
Solid to gas and gas to solid on the basis of kinetic model.
Explanation:
The kinetic molecular theory of matter states that: ... The average amount of empty space between molecules gets progressively larger as a sample of matter moves from the solid to the liquid and gas phases. There are attractive forces between atoms/molecules, and these become stronger as the particles move closer together.
A 25.0 kg probe fell freely with acceleration of 2.00 m/s^2 just before it landed on a distant planet. What is the weight of the space probe on that planet
Answer:
The weight of the probe is 50 Newtons
Explanation:
Newtons second law states that F = ma
Given the mass of 25kg, and the acceleration of 2m/s^2, we can substitute both values into the equation to find the weight force.
[tex]F = ma[/tex]
[tex]F = 25 * 2[/tex]
[tex]F = 50N[/tex]
The weight of the probe is 50 Newtons
Deepta adhivnav having weight 450N and 350N are playing see-saw. Deepta sits at a distance of 2m from the fulcrum, how far should abhinav be seated in order to balance deepta?
Answer:
Explanation:
This is a torque problem where balance is achieved when the sum of the torques equal 0. The equation for torque is
[tex]\tau=F*r[/tex] where F is the force in Newtons that is perpendicular to the lever arm, and r is the length of the lever arm in meters.
450(2) = 350r and
[tex]\frac{450(2)}{350}=r[/tex] so
r = 2.6 m
Can someone help me with this Physics question please?
Q. The half-life of tritium (hydrogen-3) is 12.3 years. If 48.0mg of tritium is released from a nuclear power plant during the course of a mishap, what mass of the sample will remain after 49.2 years?
Answer:
Explanation:
The formula for this, the easy one, is
[tex]N=N_0(\frac{1}{2})^{\frac{t}{H}[/tex] where No is the initial amount of the element, t is the time in years, and H is the half life. Filling in:
[tex]N=48.0(\frac{1}{2})^{\frac{49.2}{12.3}[/tex] and simplifying a bit:
[tex]N=48.0(.5)^4[/tex] and
N = 48.0(.0625) so
N = 3 mg left after 12.3 years
How many half-lifes is 49.2 years ?
(49.2 years) / (12.3 years per half-life) = 4 half-lifes.
In 4 half-lifes, (1/2) · (1/2) · (1/2) · (1/2) of the original sample remains.
That's (1/2⁴) or (1/16) of the original.
(1/16) of 48.0 mg = 3 mg .
=======================
Step-by-step:
== Start with 48 mg .
== After one half-life, 24 mg remains.
== Then, after the second half-life, 12 mg remains.
== Then, after the third half-life, 6 mg remains.
== Then, after the fourth half-life, 3 mg remains.
write the relation of m² with its a multiple
Explanation:
The square meter is the SI-derived unit of area. It has a symbol m² (33A1 in Unicode). It is defined as the area of a square whose sides measure exactly one metre.
URGENT
A river flows toward 90°. Mark, a riverboat
pilot, heads the boat at 297º and is able to go
straight across the river at 6.0 m/s.
a. What is the velocity of the current?
b. What is the velocity of the boat as seen
from the river bank?
which is part of the convection cycle in earths atmosphere?
a. hot, denser air rises
b. cold, denser air rises
c. hot, less-dense air rises
d. cold, less-dense air falls
what is the power of ideal sunglass
A walkway suspended across a hotel lobby is supported at numerous points along its edges by a vertical cable above each point and a vertical column underneath. The steel cable is 1.27cm in diameter and is 5.75m long before loading. The aluminum column is a hollow cylinder with an inside diameter of 16.14cm, and an unloaded length of 3.25m. When the walkway exerts a loa force of 8500N on one of the support points, through what distance does the point move down?
Answer:
[tex]\triangle I=8.60*10^{-4}m[/tex]
Explanation:
From the question we are told that:
Diameter [tex]d=1.27cm[/tex]
Length [tex]l=5.75m[/tex]
Diameter of aluminum column [tex]d_a=16.14cm[/tex]
Length of aluminum column [tex]l_a=3.25m[/tex]
Load Force [tex]F=8500N[/tex]
Generally the equation for Young modulus is mathematically given by
[tex]\gamma=\frac{FL}{A \triangle L}[/tex]
Given the The load force
[tex]F=\frac{Y_aA_a\triangle I}{L_a}+\frac{YA \triangle I}{L}[/tex]
[tex]\triangle I=\frac{F}{\frac{Y_aA_a}{L_a}}+\frac{YA}{L}[/tex]
[tex]\triangle I=\frac{8500N}{ \frac{7*10^{10} \pi (0.1624^2-0.1614^2)}{4*3.15}+ \frac{20*10^10 \pi (0.0127^2)}{4(5.75)}}[/tex]
[tex]\triangle I=8.60*10^{-4}m[/tex]
