Deck 4: Introduction to Quantum Mechanics

Question 1

Electromagnetic radiation cannot typically pass through conductive metal mesh in which the holes are smaller than the wavelength of the radiation. Which is the largest mesh that would effectively block out radiation at 5 GHz?

A) 1 m
B) 10 cm
C) 1 mm
D) 100 mm
E) 10 nm

Answer 1

C

Question 2

Femtosecond lasers can produce very short pulses of light. How long would it take a short pulse of light to travel across a 3 m table?

A) 10^-15 s
B) 10^-12 s
C) 10^-8 s
D) 10^-4 s
E) 10 s

Answer 2

C

Question 3

What is the frequency of x-ray radiation with a wavelength of 1 nm?

A) 1×10^-9 s^-1
B) 3×10^-9 s^-1
C) 1×10⁹ s^-1
D) 3×10¹⁵ s^-1
E) 3×10¹⁷ s^-1

Answer 3

E

Question 4

The index of refraction is the ratio of the speed of light in that medium to the speed of light in vacuum. If it takes a pulse of 500 nm light 0.15 ns to travel through a 3 cm block of glass, what is the index of refraction of the glass?

A) 0.0015
B) 1.5
C) 10
D) 30
E) 500

Question 5

Increasing the temperature of a black-body will cause

A) the total intensity of emitted radiation to increase
B) the peak of the emission spectrum to shift to longer wavelengths
C) the peak of the emission spectrum to shift to shorter wavelengths
D) both a & b
E) both a & c

Question 6

A laser emits 10 mJ pulses of 532 nm light. How many photons are in each pulse?

A) 2.68×10¹⁶
B) 3.73×10¹⁷
C) 2.52×10¹⁸
D) 3.73×10¹⁸
E) 5.36×10¹⁸

Question 7

Hydrogen has a strong emission line at 6563 Å. What is the energy difference between the energy levels in hydrogen that are involved in this transition?

A) 6.56×10^-10 J
B) 4.67×10^-14 J
C) 1.07×10^-19 J
D) 3.03×10^-19 J
E) 6.56×10^-19 J

Question 8

In the Franck-Hertz experiment on potassium shows a threshold occurs at 1.55 eV, what which of the following wavelengths would you expect to observe just above this threshold?

A) 155 nm
B) 374 nm
C) 400 nm
D) 600 nm
E) 800 nm

Question 9

Bohr in his model of the atom assumed that what was quantized?

A) the radius of the electron orbit
B) the energy of the electron
C) the kinetic energy of the electron
D) the angular momentum of the electron
E) the coulomb potential

Question 10

According to Bohr's model of the atom, which is the largest radius?

A) the n=1 state of H
B) the n=2 state of H
C) the n=3 state of Li²⁺
D) the n=3 state of H
E) the n=4 state of He⁺

Question 11

In the photoelectric effect, increasing the intensity of the light will

A) ensure that electrons will be emitted from all metals.
B) cause more electrons to be emitted from the metal if the frequency is sufficiently high.
C) cause the electrons to be emitted with higher kinetic energy if the frequency is sufficiently high.
D) have no effect on the experiment.
E) both b and c

Question 12

In the photoelectric effect, increasing the frequency of the light

A) cause fewer electrons to be emitted from the metal if the frequency is sufficiently high.
B) cause more electrons to be emitted from the metal if the frequency is sufficiently high.
C) cause the electrons to be emitted with higher kinetic energy if the frequency is sufficiently high.
D) have no effect on the experiment.
E) both b and c

Question 13

Estimate the de Broglie wavelength for a golf ball traveling at 10 m s^-1

A) 10^-51 m
B) 10^-35 m
C) 10^-21 m
D) 10^-6 m
E) 10 m

Question 14

What is the de Broglie wavelength of an electron traveling at 1×10⁵ m s^-1

A) 6.6×10^-39 m
B) 6.6×10^-30 m
C) 4.2×10^-18 m
D) 7.3×10^-9 m
E) 5.1×10^-8 m

Question 15

Which has a shorter wavelength: an electron with a kinetic energy of 4×10^-19 J or a photon with an energy of 4×10^-19 J?

A) the electron
B) the photon
C) they will have the same wavelength
D) there is no way to know

Question 16

Calcium has a work function of 4.64×10^-19 J. Which of the following wavelengths will eject electrons from calcium?

A) 375.2 nm
B) 401.8 nm
C) 442.4 nm
D) a & b
E) a, b, & c

Question 17

The position of an electron in a Be²⁺ ion is known to 5.0×10^-11 m. What is the uncertainty in its velocity?

A) 2.0×10⁵ m s^-1
B) 1.2×10⁶ m s^-1
C) 4.6×10⁶ m s^-1
D) 9.2×10⁶ m s^-1
E) 3.0×10⁸ m s^-1

Question 18

The uncertainty in the velocity of an electron is 1×10⁵ m s^-1. What is the minimum uncertainty in its position?

A) 5.79×10^-5 m
B) 2.31×10^-9 m
C) 5.79×10^-10 m
D) 2.31×10^-10 m
E) 1.08×10^-10

Question 19

The wave function for a n=5 state of the particle in a box has how many nodes?

A) 1
B) 3
C) 4
D) 5
E) 6

Question 20

For a particle in a cubic box, how many energy levels have an energy that is 2 times the energy of the ground state?

A) 0
B) 1
C) 2
D) 3
E) 8

Question 21

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

A) at the left edge of the box.
B) at the right edge of the box.
C) in the middle of the box.
D) the particle is equally likely to be found at all positions.
E) it depends on the energy.

Question 22

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

A) decrease by a factor of 4.
B) decrease by a factor of 2.
C) stay the same.
D) increase by a factor of 2.
E) increase by a factor of 4.

Question 23

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

A) 4.33×10¹³ Hz
B) 8.20×10¹³ Hz
C) 8.66×10¹³ Hz
D) 9.15×10¹³ Hz
E) 1.73×10¹⁴ Hz

Question 24

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?

A) 1.35×10^-21 J
B) 2.71×10^-21 J
C) 3.53×10^-21 J
D) 2.13×10^-20 J
E) 4.26×10^-20 J

Question 25

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

A) 0.25 times the radius of the n=1 orbit
B) 0.5 times the radius of the n=1 orbit
C) the same as the radius of the n=1 orbit
D) 2 times the radius of the n=1 orbit
E) 4 times the radius of the n=1 orbit

Question 26

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

A) 1
B) 0.5
C) 0.25
D) L/2
E) it depends on the quantum number n

Question 27

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?

A) 4.13×10⁵ m s^-1
B) 5.85×10⁵ m s^-1
C) 1.04×10⁶ m s^-1
D) 1.20×10⁶ m s^-1
E) no electrons will be emitted

Question 28

Which has the shortest wavelength?

A) 500 nm light
B) 10¹⁵ Hz light
C) an electron traveling at 2×10⁵ m s^-1
D) a 10 g mass traveling at 10 m s^-1
E) there is no way to know

Question 29

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

A) n=1 electron in He⁺
B) n=2 electron in H
C) n=2 electron in He⁺
D) n=3 electron in Li²⁺
E) n=3 electron in H

Question 30

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

A) 8 to 9
B) 9 to 8
C) 3 to Ö8
D) Ö8 to 3
E) they are the same

Question 31

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

A) The amplitude of the wave
B) The frequency of the wave
C) The wavelength of the wave
D) A and B
E) B and C

Question 32

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

A) ultraviolet
B) X-rays
C) microwave
D) infrared
E) -rays

Question 33

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

A)
B)
C)
D)
E)