Vibrations in the diatomic molecule CO can be approximated as a harmonic oscillator, where the angular frequency w = 6.505 x 1013 Hz and the reduced mass is equal to u = 1.14 x 10-27 kg. Assume the molecule is in its first excited vibrational state. Its vibrational wavefunction can then be written as w1(x) = (/)^(1/4) (2xe) ^ -ax^2/2 where = /h we were to measure the bond length of the molecule, what is the most likely displacement from the equilibrium bond distance in the first excited vibrational state? Give your answer in Angstroms [Note: The equilibrium displacement in the Quantum harmonic oscillator corresponds to x = = 0, ie the coordinate x measures displacement from equilibrium]

Vibrations in the diatomic molecule CO can be approximated as a harmonic oscillator, where the angular frequency w = 6.505 x 1013 Hz and the reduced mass is equal to u = 1.14 x 10-27 kg. Assume the molecule is in its first excited vibrational state. Its vibrational wavefunction can then be written as w1(x) = (〖∝/π)〗^(1/4) √(2∝xe) ^ -ax^2/2 where ∝ = μω/h we were to measure the bond length of the molecule, what is the most likely displacement from the equilibrium bond distance in the first excited vibrational state? Give your answer in Angstroms [Note: The equilibrium displacement in the Quantum harmonic oscillator corresponds to x = = 0, ie the coordinate x measures displacement from equilibrium]

Answers

Answer 1

The CO molecule's initial excited vibrational state has a displacement from the equilibrium bond distance that is most likely 0.2262 Angstroms.

Why should a diatomic molecule be thought of as a harmonic oscillator?

A diatomic molecule vibrates similar to two masses being supported by a spring, and its potential energy is proportional to the square of the deviation from equilibrium. But the quantized energy levels have values that are evenly spaced apart. The frequency in this form corresponds to the simple harmonic oscillator's traditional form.

[tex]x = √(h/2μω)(2(1)+1/2) = √(h/2(1.14x10^-27 kg)(6.505x10^13 Hz))(3/2)[/tex]

[tex]x = 2.262 x 10^-11 meters[/tex]

Converting to angstroms, we get:

x = 0.2262 Angstroms (rounded to 4 decimal places)

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The following is used to process and display browser database application forms, reports, and queries: Web Application Server (WAS) is a server that uses web application server technology to deliver web-based applications.

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Identify ways that you can save energy. For example, walking up a floor instead of taking the elevator, or walking or riding your bike an hour a day instead of taking the car. Estimate the amount of energy that you could save every year with your proposal. Also, estimate the amount of fuel that can be saved in the same manner. State your assumptions, and present your detailed analysis in a report.

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Energy saved = 21,900 kWh per year

Fuel Saved = 730 liters

Let's dive deeper into the details below.

One can save energy in various ways, such as walking up a floor instead of taking the elevator, walking, or riding a bike for an hour a day instead of driving a car. Here are some ways in which energy can be saved:

1. Turning off lights and electronics when they're not in use

2. Using energy-efficient light bulbs

3. Reducing water usage

4. Using public transportation, biking, or walking instead of driving a car

5. Installing a programmable thermostat

6. Purchasing energy-efficient appliances

7. Using natural light to save energy

8. Properly insulating homes to save energy

9. Upgrading to energy-efficient windows and doors

10. Planting trees and shrubs to shade your home and keep it cool during the summer.

11. Weatherizing your home to keep heat in during the winter.

Assumptions: Let's assume that there are three floors in a building, and each floor has five rooms, and each room has four tube lights (40 watts each) that run for ten hours each day. Now, if we replace these tube lights with LED lights, which consume ten watts each, we can save 30*5*4*40 = 60,000 watts per day.

It will be equal to 60 kWh per day or 21,900 kWh per year.

Assumptions: Let's assume that you drive 20 km every day, and your car's average fuel consumption is 10 km per liter of petrol. If you ride a bicycle instead of driving a car for one hour each day, you can save 20/10 = 2 liters of petrol per day.

It will be equal to 730 liters of petrol per year.

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