Question 1

For the a particle in a box in the n = 1 state, you are most likely to find the particle

Accepted Answer

For a particle in a box in the n = 1 state, the probability density is highest in the middle of the box, making it most likely to find the particle there.

Question 2

For the one dimensional particle in a box if you double the length of the box the ground state energy will

Accepted Answer

The ground state energy of a particle in a box is inversely proportional to the square of the length of the box. Doubling the length decreases the energy by a factor of 4.

Question 3

If the vibrational frequency of H³⁵Cl is 8.66×10¹³ Hz, what do you think the vibrational frequency of H³⁷Cl would be?

Accepted Answer

The vibrational frequency of a diatomic molecule is inversely proportional to the square root of its reduced mass. The reduced mass of H³⁵Cl is 1.626×10^-27 kg, and the reduced mass of H³⁷Cl is 1.636×10^-27 kg. Therefore, the vibrational frequency of H³⁷Cl would be 8.66×10¹³ Hz / √(1.626×10^-27 kg / 1.636×10^-27 kg) = 8.20×10¹³ Hz.

Question 4

If the bond in carbon monoxide is modeled as a harmonic oscillator the force constant is 1860 N m^-¹, and the reduced mass is 6.86 amu. What is the energy of the ground vibrational state of CO?

Accepted Answer

The answer of If the bond in carbon monoxide is...

Question 5

In Bohr's model of the atom the radius of an electron in the n=2 orbit is

Accepted Answer

In Bohr's model, the radius of an electron orbit is proportional to the square of the principal quantum number, n. Therefore, for n=2, the radius is 2^2 = 4 times the radius of the n=1 orbit.

Question 6

What is the probability of finding a particle in a box of length L between zero and L/2?

Accepted Answer

The probability of finding a particle in a box of length L between zero and L/2 is 0.5. This is because the particle is equally likely to be found anywhere in the box, and the probability of finding it in any given region is proportional to the length of that region.

Question 7

The work function for aluminum is 6.53×10^-¹⁹ J. If a surface of aluminum is irradiated with 400 nm what is the maximum kinetic energy of the electrons emitted from the surface due to the photo-electric effect?

Accepted Answer

The energy of the incident photons (3.1×10^-19 J) is less than the work function of aluminum (6.53×10^-19 J), so no electrons will be emitted.

Question 8

Which has the shortest wavelength?

Accepted Answer

The answer of Which has the shortest wavelength?
...

Question 9

According to the Bohr model of the atom, which is highest in energy?

Accepted Answer

The answer of According to the Bohr model of the...

Question 10

Assuming they have the same force constant, the ratio the vibrational frequency for ¹⁶O₂ to ¹⁸O₂ is

Accepted Answer

The answer of Assuming they have the same force constant,...

Question 11

The energy of electromagnetic radiation is directly proportional to...

Accepted Answer

The answer of The energy of electromagnetic radiation is directly...

Question 12

Radiation from which region of the electromagnetic spectrum will induce molecular vibrations without inducing electronic transitions?

Accepted Answer

Infrared radiation has the right energy to cause molecular vibrations, such as stretching and bending of bonds, without having enough energy to induce electronic transitions.

Question 13

Proper wavefunctions ( ψ ) in quantum mechanics must be normalized. Which statement below best summarizes this mathematically?

Accepted Answer

The normalization condition for a wavefunction is that the integral of the square of the wavefunction over all space equals 1.

Quiz 4: Introduction to Quantum Mechanics