Deck 7: Quantum Theory

Question 1

The red radiation emitted by a HeNe laser is of wavelength 6328 Å. Calculate the energy of the photons that are emitted.

A) 3.139  10^-19 J
B) 3.139  10^-29 J
C) 4.193  10^-40 J
D) 4.193  10^-20 J

Answer 1

A

Question 2

Ultraviolet radiation of wavelength 121 nm is used to irradiate a sample of potassium metal. The work function of potassium is 2.25 eV. Calculate the speed of the electrons emitted through the photoelectric effect.

A) 1.89  10⁶ m s^-1
B) 1.18  10⁶ m s^-1
C) 0.890  10⁶ m s^-1
D) 1.68  10⁶ m s^-1

Answer 2

D

Question 3

Estimate the de Broglie wavelength of a neutron that has a kinetic energy of 0.025 eV.

A) 1.8 Å
B) 78 Å
C) 7.0  10⁶ m
D) 72  10^-21 m

Answer 3

A

Question 4

A photoelectron produced by ionization in a photoelectron spectrometer is ejected with a velocity of 861 km s^-1. Calculate the de Broglie wavelength of the electron.

A) 8.45 nm
B) 8.45 Å
C) 8.45 pm
D) 0.845 m

Question 5

A  electron in a conjugated hydrocarbon is confined to an effective distance of 8.27 Å. Use the uncertainty principle to calculate the minimum uncertainty in the speed of the electron.

A) 44.0 km s^-1
B) 7.00  10^-6 m s^-1
C) 70.0 km s^-1
D) 1.46  10¹⁶ m s^-1

Question 6

The effective length of the  system in the conjugated linear hydrocarbon hexa-1,3,5-triene, C₆H₈, is 7.4 Å. By treating the  electrons as particles in a one-dimensional box, calculate the wavelength of the lowest energy absorption in the electronic spectrum of hexa-1,3,5-triene.

A) 260 nm
B) 1820 nm
C) 140 nm
D) 202 nm

Question 7

A quantum-mechanical particle of mass m is contained within a three-dimensional box with all sides of the same length L. What is the degeneracy of the level with energy 9h² / 8mL²?

A) 9
B) 2
C) 1
D) 6

Question 8

For a particle rotating in three dimensions, what is the degeneracy of the level with orbital angular momentum quantum number l = 3?

A) 1
B) 0
C) 7
D) 2

Question 9

A quantum-mechanical particle rotating in three dimensions has an orbital angular momentum quantum number l = 2. What is the magnitude of the angular momentum?

A) 2 kg m²
B) 2 ℏ
C) 3 ℏ
D) 6^1/2 ℏ

Question 10

The vibrational energy of a carbon monoxide, CO, molecule in its first excited vibrational state is 3.42  10^-20 J. Assuming that a carbon monoxide molecule may be treated as a harmonic oscillator with a force constant of k = 2170 N m^-1, calculate the classical amplitude of vibration for the molecule in this state.

A) 5.61 nm
B) 5.61 pm
C) 5.61 Å
D) 56.1 nm