Deck 28: Quantum Physics

Question 1

The light intensity incident on a metallic surface produces photoelectrons with a maximum kinetic energy of 2 eV.The light intensity is doubled.Determine the maximum kinetic energy of the photoelectrons (in eV).

A)4
B)2
C) $\sqrt { 2 }$
D)3
E)16

Answer 1

2

Question 2

The experimental observation(s)below that require(s)a quantum explanation for the photoelectric effect

A)is that more photoelectrons are emitted when the light frequency increases.
B)is that the maximum kinetic energy of the photoelectrons is related linearly to the frequency of the light.
C)is that every metal surface has a work function,a minimum amount of energy needed to free electrons.
D)is that the stopping potential measures the kinetic energy of the photoelectrons.
E)are all of the above.

Answer 2

is that the maximum kinetic energy of the photoelectrons is related linearly to the frequency of the light.

Question 3

What is the maximum kinetic energy (in eV)of a photoelectron when a surface,whose work function is 5.0 eV,is illuminated by photons whose wavelength is 400 nm?

A)3.1
B)-1.9
C)1.9
D)0
E)1.2

Answer 3

0

Question 4

Your temperature is 98.6 $\degree$ F.Assuming your skin is a perfect radiator ( $\varepsilon$ = 1),determine the wavelength corresponding to the largest intensity (in $\mu$ m).

A)8.0
B)9.3
C)3.0
D)5.7
E)29.4

Question 5

A 15-kg mass,attached to a massless spring whose force constant is 2 500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if E_n = nhf.

A)1.5 * 10³³
B)3.0 *10³³
C)4.5 *10³³
D)5.4 *10³³
E)1.0 *10³³

Question 6

What is the maximum velocity (in km/s)of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

A)460
B)650
C)420
D)550
E)1 480

Question 7

Assume electrons are accelerated through a potential difference of 25 000 V inside a TV picture tube.What is the minimum wavelength that could be produced when the electrons strike the phosphor? (1 Å = 10 ^{- 10} m)

A)0.50 Å
B)1.0 Å
C)10 Å
D)100 Å
E)0.25 Å

Question 8

In an experiment different wavelengths of light,all able to eject photoelectrons,shine on a freshly prepared (oxide-free)zinc surface.Which statement is true?

A)The number of photoelectrons emitted per second is independent of the intensity of the light for all the different wavelengths.
B)The number of photoelectrons emitted per second is directly proportional to the frequency for all the different wavelengths.
C)The maximum kinetic energy of the photoelectrons emitted is directly proportional to the frequency for each wavelength present.
D)The maximum kinetic energy of the photoelectrons has a linear relationship with the frequency for each wavelength present.
E)The maximum kinetic energy of the photoelectrons is proportional to the intensity of the light and independent of the frequency.

Question 9

How much energy is in an 89.7 MHz photon of FM-radiation?

A)2.2 *10^-33 J
B)9.5 *10^-27 J
C)7.4 * 10^-42 J
D)5.9 *10^-26 J
E)3.7 *10^-25 J

Question 10

How much energy is in a 63 kHz photon of AM-radiation?

A)1.0 *10^-38 J
B)6.6 *10^-30 J
C)4.2 *10^-29 J
D)3.1 * 10^-30 J
E)13 *10^-29 J

Question 11

A stopping potential of 3.2 V is needed for radiation whose wavelength is 200 nm.What is the work function (in eV)of the material?

A)4.0
B)3.0
C)5.0
D)6.0
E)2.0

Question 12

The threshold wavelength for photoelectric emission of a particular substance is 500 nm.What is the work function (in eV)?

A)4.2
B)4.0 *10 ^{- 19}
C)4.0 *10 ^{- 10}
D)2.5 *10 ^{- 19}
E)2.5

Question 13

What is the maximum kinetic energy (in eV)of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

A)1.9
B)1.2
C)3.1
D)zero
E)6.2

Question 14

The number of photons per second passing a plane perpendicular to a collimated monochromatic (one frequency)beam of light transporting power P is directly proportional to

A)the wavelength of the light.
B)the frequency of the light.
C)the power of the beam.
D)all of the above.
E)only (a)and (c)above.

Question 15

A solid state pulsed laser has an energy of 400 mJ per pulse.If its wavelength is 1.06 *10 ^{- 6} m,how many photons are in each pulse?

A)2*10²⁵
B)2 *10²¹
C)3 *10¹⁸
D)6 * 10³⁸
E)2 * 10¹⁸

Question 16

A pendulum located where $g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }$ has a 0.500 kg bob and a 4.00 Hz oscillation frequency.If it is released from a point 0.150 m above the lowest point it reaches,the number of quanta in this oscillation is

A)2.77 * 10³².
B)1.11 * 10³³.
C)4.87 *10 ^{- 34}.
D)0.184.
E)4.00.

Question 17

Photoelectrons are ejected when monochromatic light shines on a freshly-prepared (oxide-free)sodium surface.In order to obtain the maximum increase in the number of electrons ejected per second,the experimenter needs to

A)increase the frequency of the light.
B)increase the intensity of the light.
C)increase the area illuminated by the light.
D)do all of the above.
E)do only (b)and (c)above.

Question 18

A helium-neon laser emits red light having a wavelength of 6.4 *10 ^{- 7} m and a power of 0.5 mW.How many photons are emitted each second?

A)6.4 * 10³⁸
B)1.6 * 10²¹
C)3.2 * 10²⁵
D)2.6 * 10¹⁸
E)1.6 *10¹⁵

Question 19

A photon whose energy is 8.00 *10 ^{- 15} J is scattered off an electron at a 90 $\degree$ angle.What is the wavelength of the scattered wave?

A)2.73 *10 ^{- 11} m
B)2.25 *10 ^{- 11} m
C)2.50 *10 ^{- 11} m
D)2.40 *10 ^{- 12} m
E)2.48 *10 ^{- 11} m

Question 20

The light intensity incident on a metallic surface with a work function of 3 eV produces photoelectrons with a maximum kinetic energy of 2 eV.The frequency of the light is doubled.Determine the maximum kinetic energy (in eV).

A)3
B)2
C) $\sqrt { 2 }$
D)4
E)7

Question 21

A neutron has a mass of 1.67 *10 ^{- 27} kg.Its de Broglie wavelength is 1.4 *10 ^{- 10} m.What is its kinetic energy (in eV)?

A)4
B)0.4
C)0.04
D)40
E)0.08

Question 22

Assume the Heisenberg uncertainty principle can take the form $\Delta$ E $\Delta$ t $\ge$ h/4B.How accurate can the position of an electron be made if its speed is 5 * 10⁶ m/s and if the uncertainty in its energy is 10 eV?

A)7.7 *10 ^{- 18} m
B)1.3 *10 ^{- 23} m
C)6.2 * 10 ^{- 15} m
D)1.6 *10 ^{- 10} m
E)1.2 *10 ^{- 9} m

Question 23

Because the factor h on the right side of the Heisenberg uncertainty principle has units of Joule-seconds,it suggests that the energy of a system also has uncertainty.The uncertainty in energy depends on the length of the time interval during which a system exists. $\Delta$ E $\Delta$ t $\ge$ h/4 $\pi$ .Suppose an unstable mass is produced during a high-energy collision such that the uncertainty in its mass is m_e/100.(m_e = 9.11 *10 ^{- 31} kg. )How long will this particle exist?

A)6.4 * 10 ^{- 20} s
B)2.3 *10 ^{- 23} s
C)1.0 * 10¹⁵ s
D)1.2 * 10¹³ s
E)8.1 * 10 ^{- 19} s

Question 24

An electron has been accelerated by a potential difference of 100 V.If its position is known to have an uncertainty of 1 nm,what is the percent uncertainty ( $\Delta$ p/p * 100)of the electron?

A)1%
B)2%
C)10%
D)>>10%
E)5%

Question 25

A neutron has a mass of 1.67 *10 ^{- 27} kg.The de Broglie wavelength is 1.4 *10 ^{- 10} m.How fast is the neutron going? (in m/s)

A)3.4 *10³
B)2.8 * 10³
C)3.9 * 10³
D)2.6 * 10³
E)1.7 * 10³

Question 26

Light can exhibit the characteristics of

A)a particle with energy E = hf.
B)a wave with wavelength $\lambda = \frac { h c } { E }$ .
C)a particle or wave that travels at speed $c = 3.00 \times 10 ^ { 8 } \frac { \mathrm { m } } { \mathrm { s } }$ in all materials.
D)all of the above.
E)only (a)or (b)above.

Question 27

Film behind a double slit is exposed to light in the following way: First one slit is opened and light is allowed to go through that slit for time $\Delta$ t.Then it is closed and the other slit is opened and light is allowed to go through that slit for the same time $\Delta$ t.When the film is developed the pattern will be

A)one single slit pattern.
B)two superimposed single slit patterns,their centers displaced from each other by the distance between the two slits.
C)one double slit pattern.
D)two double slit patterns,their centers displaced from each other by the distance between the two slits.
E)random darkening of the film.(no pattern at all)

Question 28

In electron diffraction,an electron moving at speed v << c acts like

A)a particle with momentum mv.
B)a particle with position coordinate v/t.
C)a wave with wavelength v/t.
D)a wave with wavelength h/mv.
E)both a particle with position coordinate v/t and a wave with wavelength v/t.

Question 29

When a photon collides with a free electron at rest and the direction of motion of the photon changes,

A)the magnitude of the momentum of the photon does not change.
B)the momentum of the electron does not change.
C)the kinetic energy of the electron does not change.
D)the total energy of the photon does not change.
E)both the magnitude of the momentum and the total energy of the photon decrease.

Question 30

A photon whose wavelength is = 5.0 * 10 ^{- 11} m is scattered straight backward.What is the wavelength of the scattered wave?

A)5.0 *10 ^{- 11} m
B)4.5 *10 ^{- 11} m
C)5.5 *10 ^{- 11} m
D)6.0 *10 ^{- 11} m
E)6.5 *10 ^{- 11} m

Question 31

A wave packet can represent a quantum particle because

A)it has the localized nature of a particle.
B)the group velocity is identical to the speed of the particle.
C)the waves that compose the packet can show interference and diffraction.
D)of all of the above.
E)of only (a)and (b)above.

Question 32

The wavelength of a 45-kg teenager moving at 5 m/s on a skateboard is about

A)5*10 ^{- 37} m.
B)3 *10 ^{- 36} m.
C)7 *10 ^{- 34} m.
D)0.1 m.
E)5 m.

Question 33

Microscopes are inherently limited by the wavelength of the light used.How much smaller (in order of magnitude)can we "see" using an electron microscope whose electrons have been accelerated through a potential difference of 50 000 V than using red light (500 nm)?

A)3
B)4
C)5
D)6
E)14

Question 34

Light behaves like

A)a wave at times,and a particle at other times.
B)a wave.
C)a particle.
D)both a wave and a particle,because of its dual nature.

Question 35

A quantum particle

A)can be localized in space.
B)can be represented by an infinitely long wave having a single frequency.
C)can be represented by a wave packet.
D)travels at the phase speed of the infinitely long wave having the highest frequency.
E)has the highest probability of being present in those regions of space where its component waves interfere destructively.

Question 36

Assume we can determine the position of a particle within an uncertainty of 0.5 nm.What will be the resulting uncertainty in the particle's momentum (in kg . m/s)?

A)1.9 *10^-25
B)4.2 *10^-25
C)1.1 * 10^-25
D)1.3 * 10^-24
E)6.6 * 10^-25

Question 37

A photon collides with an electron.After the collision the wavelength of the scattered wave at a scattering angle greater than $0 ^ { \circ }$ is

A)greater than or equal to the initial wavelength.
B)equal to the initial wavelength.
C)less than or equal to the initial wavelength.
D)greater than the initial wavelength.
E)less or greater depending on the scattering angle.

Question 38

Find the uncertainty in the momentum (in kg . m/s)of an electron if the uncertainty in its position is equal to 3.4 *10 ^{- 10} m,the circumference of the first Bohr orbit.

A)6.2 *10 ^{- 25}
B)1.6 *10 ^{- 25}
C)15.5 * 10 ^{- 25}
D)19.4 *10 ^{- 25}
E)2.0 *10 ^{- 24}

Question 39

An electron is accelerated through a potential difference of 25 000 V.What is the de Broglie wavelength of the electron (in m)?

A)5.9 *10 ^{- 12}
B)6.8 *10 ^{- 12}
C)6.5*10 ^{- 12}
D)7.8 *10 ^{- 12}
E)5.5 *10 ^{- 12}

Question 40

A neutron has a mass of 1.67 *10 ^{- 27} kg.Its de Broglie wavelength is 1.4 *10 ^{- 10} m.What temperature would it correspond to if we had a monatomic gas having the same average kinetic energy (in $\degree$ C)?

A)273
B)25
C)36
D)309
E)51

Question 41

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its energy is 2 h²/mL²?

A)2
B)8
C)4
D)1
E)16

Question 42

A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg .m/s)?

A)9.9 *10 ^{- 34}
B)6.6 *10 ^{- 34}
C)3.3*10 ^{- 34}
D)13 *10 ^{- 34}
E)cannot be solved unless mass of particle is known.

Question 43

A particle is in the first excited state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg . m/s)?

A)3.3 *10 ^{- 34}
B)6.6 *10 ^{- 34}
C)9.9 *10 ^{- 34}
D)13 *10 ^{- 34}
E)22 *10 ^{- 34}

Question 44

Frank says that quantum mechanics does not apply to baseballs because they do not jump from quantum state to quantum state when being thrown.Francine agrees with him.She says that there is no uncertainty in a baseball's position or momentum.Are they correct,or not,and why?

A)They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives.Therefore we cannot determine whether or not there is uncertainty in its position or momentum.
B)They are correct because the first excited state of a baseball is at a higher energy that any baseball ever receives.Therefore its position and momentum are completely uncertain until it is caught.
C)They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions.The uncertainties in its position and momentum are too small to observe.
D)They are wrong because the baseball goes through so many quantum states in being thrown that we cannot observe the transitions.Because of the number of transitions its position and momentum are completely uncertain until it is caught.
E)Quantum mechanics states that they are correct as long as they do not make any observations,but wrong as soon as they begin to make observations.

Question 45

A baseball (1 kg)has an energy of 100 joules.If its uncertainty in position is 1 m,what is the percentage uncertainty ( $\Delta$ p/p * 100)in the momentum of the baseball?

A)<<1%
B)1%
C)2%
D)5%
E)10%

Question 46

The wave function for a particle in a one-dimensional box is $\Psi = A \sin \left( \frac { n \pi x } { L } \right)$ .Which statement is correct?

A)This wavefunction gives the probability of finding the particle at x.
B)| $\Psi$ (x)|² gives the probability of finding the particle at x.
C)| $\Psi$ (x)|² $\Delta$ x gives the probability of finding the particle between x and x + $\Delta$ x.
D) $\int _ { 0 } ^ { L } \Psi ( x ) d x$ gives the probability of finding the particle at a particular value of x.
E) $\int _ { 0 } ^ { L } | \Psi ( x ) | ^ { 2 } d x$ gives the probability of finding the particle between x and x + $\Delta$ x.

Question 47

If the interaction of a particle with its environment restricts the particle to a finite region of space,the result is the quantization of ____ of the particle.

A)the momentum
B)the energy
C)the velocity
D)all of the above properties
E)only properties (a)and (b)

Question 48

Find the kinetic energy (in terms of Planck's constant)of a baseball (m = 1 kg)confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state.

A)3 h²
B)2 h²
C)h²
D)4h²
E)0.5 h²

Question 49

When U(x)is infinitely large elsewhere,the wave function of a particle restricted to the region 0 < x < L where U(x)= 0,may have the form $\Delta$ (x)=

A) $A \sin \left( \frac { n \pi x } { L } \right)$ .
B) $B \cos \left( \frac { n \pi x } { L } \right)$ .
C)Ae^{n $\pi$ x / L}.
D) $A \sin \left( \frac { n \pi x } { L } \right) + B \cos \left( \frac { n \pi x } { L } \right)$ .
E) $A \sin \left( \frac { n \pi x } { L } \right) - B \cos \left( \frac { n \pi x } { L } \right)$ .

Question 50

The fact that we can only calculate probabilities for values of physical quantities in quantum measurements means that

A)radiation and matter are not described by mathematical relations between measurements.
B)the probabilities cannot be calculated from mathematical relationships.
C)the results of physical measurements bear no relationship to theory.
D)the average values of a large number of measurements correspond to the calculated probabilities.
E)the average of the values calculated in a large number of different theories corresponds to the results of a measurement.

Question 51

Calculate the ground state energy (in eV)for an electron in a box (an infinite well)having a width of 0.050 nm.

A)10
B)75
C)24
D)150
E)54

Question 52

A physically reasonable wave function, $\Psi$ (x),for a one-dimensional system must

A)be defined at all points in space.
B)be continuous at all points in space.
C)be single-valued.
D)obey all the constraints listed above.
E)obey only (b)and (c)above.

Question 53

When the potential energy of a system is independent of time,the wave function of the system

A)is a constant.
B)is directly proportional to the time.
C)cannot be normalized.
D)depends only on the center of mass, $\overrightarrow { \mathrm { R } }$ ,of the system.
E)depends on the vector positions, $\overrightarrow { \mathbf { r } }$ _i,of each particle in the system.

Question 54

Because of Heisenberg's Uncertainty Principle,the velocity of a particle is known least precisely when the length of the wave packet representing the particle is

A)< 10 ^{- 15} m.
B)< 10 ^{- 10} m.
C)of the order of 1.00 m.
D)>10 m.
E)the length of a plane wave (infinite)

Question 55

The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by $\Psi$ (x)= A sin (n $\pi$ x/L)+ B cos (n $\pi$ x/L).The constants A and B are determined to be

A) $\sqrt { 2 / L }$ ,0
B) $\sqrt { 1 } / L$ , $\sqrt { 1 / L }$
C)0, $\sqrt { 2 / L }$
D) $\sqrt { 2 } / L$ , $\sqrt { 2 / L }$
E)2/L,0

Question 56

If the position of an electron (m = 9.11 *10 ^{- 31} kg)could be measured to within 10 ^{- 30} m,the uncertainty in the magnitude of its speed could be as much as

A)6 *10 ^{- 34} m/s.
B)6 *10²⁵ m/s.
C)6 * 10³⁰ m/s.
D)10³¹ m/s.
E)10⁶¹ m/s.

Question 57

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

A)1
B)4
C)2
D)8
E)16

Question 58

The expectations value of a function f(x)of x when the wave function depends only on x is given by < f(x)> =

A) $\int _ { - \infty } ^ { + \infty } \sqrt { f ( x ) } \psi ( x ) d x$ .
B) $\int _ { - \infty } ^ { + \infty } f ( x ) \psi ( x ) d x$ .
C) $\int _ { - \infty } ^ { + \infty } f ( x ) \psi ^ { * } ( x ) d x$ .
D) $\int _ { - \infty } ^ { + \infty } \psi ^ { * } ( x ) f ( x ) \psi ( x ) d x$ .
E) $\int _ { - \infty } ^ { + \infty } \psi ^ { * } ( x ) \frac { f ^ { 2 } ( x ) } { 2 } \psi ( x ) d x$ .

Question 59

The average position,or expectation value,of a particle whose wave function $\Psi$ (x)depends only on the value of x,is given by < x > =

A) $\int _ { - \infty } ^ { + \infty } \sqrt { x } \psi ( x ) d x$ .
B) $\int _ { - \infty } ^ { + \infty } x \psi ( x ) d x$ .
C) $\int _ { - \infty } ^ { + \infty } \frac { x } { 2 } \psi ^ { 2 } ( x ) d x$ .
D) $\int _ { - \infty } ^ { + \infty } \frac { x ^ { 2 } } { 2 } \psi ( x ) d x$ .
E) $\int _ { - \infty } ^ { + \infty } \psi ^ { * } ( x ) x \psi ( x ) d x$ .

Question 60

A particle is in the second excited state of a one-dimensional box of length 1.0 m.What is its momentum (in kg . m/s)?

A)6.6 *10 ^{- 34}
B)3.3 *10 ^{- 34}
C)9.9 * 10 ^{- 34}
D)13 *10 ^{- 34}
E)cannot be solved unless mass of particle is known

Question 61

Quantum tunneling occurs in

A)nuclear fusion.
B)radioactive decay by emission of alpha particles.
C)the scanning tunneling microscope.
D)all of the above.
E)only (b)and (c)above.

Question 62

An electron is sitting on a pinpoint having a diameter of 2.5 $\mu$ m.What is the minimum uncertainty in the speed of the electron?

Question 63

What is the energy in eV of a photon of yellow light? $\lambda$ = 500 nm.

Question 64

What is the shortest x-ray wavelength that can be produced in a 12-keV x-ray machine?

Question 65

Suppose we use optical radiation ( $\lambda$ = 500 nm)to determine the position of the electron to within the wavelength of the light.What will be the resulting uncertainty in the electron's velocity?

Question 66

Classically,the concept of "tunneling" is impossible.Why?

A)The kinetic energy of the particle would be negative.
B)The velocity of the particle would be negative.
C)The total energy of a particle is equal to the kinetic and potential energies.
D)The kinetic energy must be equal to the potential energy.
E)The total energy for the particle would be negative.

Question 67

If a rubidium surface is irradiated with blue light of wavelength 450.0 nm,what is the kinetic energy of the electrons emitted? (The work function for rubidium is $\phi$ = 2.09 eV. )

Question 68

On a bright and sunny day,the intensity of solar radiation on the Earth's surface is 1 000 W/m².If the average wavelength of the sunlight is 500 nm,how many photons are incident on a square meter of the Earth's surface per second?

Question 69

The "seeing ability" or resolution of radiation is determined by its wavelength.If an atom is approximately 10 ^{- 10} m in diameter,how fast must an electron travel to have a wavelength smaller than the size of an atom?