Question 1

Protons are being accelerated in a particle accelerator. When the speed of the protons is doubled, their de Broglie wavelength will
A) increase by a factor of 4.
B) increase by a factor of 2.
C) decrease by a factor of 2.
D) increase by a factor of $\sqrt { 2 }$ .
E) decrease by a factor of $\sqrt { 2 }$ .

Accepted Answer

The de Broglie wavelength is inversely proportional to the momentum of the particle. Doubling the speed of the protons doubles their momentum, thus halving the wavelength.

Question 2

Monochromatic light falls on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons?
A) greater rate; same maximum energy.
B) same rate; greater maximum energy.
C) greater rate; greater maximum energy.
D) same rate; same maximum energy.

Accepted Answer

The ejection rate of electrons increases with the intensity of the light because more photons are hitting the surface, leading to more electrons being ejected. However, the maximum energy of the ejected electrons is determined by the frequency of the light, not its intensity, and remains the same as the intensity is increased.

Question 3

When the surface of a metal is exposed to blue light, electrons are emitted. If the intensity of the blue light is increased, which of the following things will also increase?
A) the number of electrons ejected per second
B) the maximum kinetic energy of the ejected electrons
C) the time lag between the onset of the absorption of light and the ejection of electrons
D) the work function of the metal
E) all of the above

Accepted Answer

Increasing the intensity of the blue light increases the number of photons hitting the metal surface per second, which in turn increases the number of electrons ejected per second. The maximum kinetic energy of the ejected electrons and the work function of the metal are properties dependent on the frequency of the light, not its intensity. There is no time lag between the absorption of light and the ejection of electrons in the photoelectric effect.

Question 4

If a proton and an electron have the same de Broglie wavelengths, which one is moving faster?
A) the electron
B) the proton
C) They both have the same speed.

Accepted Answer

The de Broglie wavelength is given by λ = h/mv, where h is the Planck constant, m is the mass of the particle, and v is its velocity. Since the masses of the proton and electron are different, if they have the same de Broglie wavelength, their velocities must be different. Therefore, the electron, which has a smaller mass, must be moving faster than the proton.

Question 5

A blue laser beam is incident on a metallic surface, causing electrons to be ejected from the metal. If the frequency of the laser beam is increased while the intensity of the beam is held fixed,
A) the rate of ejected electrons will decrease and their maximum kinetic energy will increase.
B) the rate of ejected electrons will remain the same but their maximum kinetic energy will increase.
C) the rate of ejected electrons will increase and their maximum kinetic energy will increase.
D) the rate of ejected electrons will remain the same but their maximum kinetic energy will decrease.

Accepted Answer

The ejection of electrons from a metal surface is governed by the photoelectric effect, which states that the kinetic energy of ejected electrons is proportional to the frequency of the incident light. Therefore, as the frequency of the laser beam is increased while the intensity is held fixed, the maximum kinetic energy of the ejected electrons will increase. However, since the intensity is held fixed, the number of ejected electrons will not increase proportionally, resulting in a decrease in the rate of ejected electrons. Thus, option A is the best choice.

Question 6

If a proton and an electron have the same speed, which one has the longer de Broglie wavelength?
A) the electron
B) the proton
C) It is the same for both of them.

Accepted Answer

The de Broglie wavelength of a particle is inversely proportional to its mass. Since the mass of the electron is much smaller than that of the proton, the electron will have a longer de Broglie wavelength than the proton at the same speed.

Question 7

Which of the following actions will increase the de Broglie wavelength of a speck of dust? (There could be more than one correct choice.)
A) Increase its mass.
B) Increase its speed.
C) Decrease its mass.
D) Decrease its speed.
E) Decrease its momentum.

Accepted Answer

The answer of Which of the following actions will increase...

Question 8

Two sources emit beams of microwaves. The microwaves from source A have a frequency of 10 GHz, and the ones from source B have a frequency of 20 GHz. This is all we know about the two beams. Which of the following statements about these beams are correct? (There could be more than one correct choice.)
A) Beam B carries twice as many photons per second as beam A.
B) A photon in beam B has twice the energy of a photon in beam A.
C) The intensity of beam B is twice as great as the intensity of beam A.
D) A photon in beam B has the same energy as a photon in beam A.
E) None of the above statements are true.

Accepted Answer

The energy of a photon is directly proportional to the frequency, according to the formula E=hf, where E is energy, h is Planck's constant, and f is frequency. Therefore, since beam B has twice the frequency of beam A, a photon in beam B has twice the energy of a photon in beam A. The number of photons per second and the intensity of the beams cannot be determined from the frequency information given.

Question 9

Protons are being accelerated in a particle accelerator. When the energy of the protons is doubled, their de Broglie wavelength will
A) increase by a factor of 4.
B) increase by a factor of 2.
C) decrease by a factor of 2.
D) increase by a factor of $\sqrt { 2 }$ .
E) decrease by a factor of $\sqrt { 2 }$ .

Accepted Answer

The de Broglie wavelength of a particle is given by $\lambda = h/p$, where $h$ is Planck's constant and $p$ is the momentum of the particle. Since momentum is directly proportional to the square root of energy, doubling the energy of the protons will increase their momentum by a factor of $\sqrt{2}$. Therefore, their de Broglie wavelength will decrease by a factor of $\sqrt{2}$.

Question 10

Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal you should
A) use light of a longer wavelength.
B) use light of a shorter wavelength.
C) use light of the same wavelength but increase its intensity.
D) use light of the same wavelength but decrease its intensity.

Accepted Answer

The photoelectric effect states that electrons will only be emitted from a metal surface if the incident light has a frequency (or wavelength) higher than a certain threshold value. Therefore, using light of a shorter wavelength (higher frequency) will increase the energy of the photons, and if the threshold frequency is exceeded, the electrons will be ejected from the metal surface.

Question 11

If the wavelength of a photon in vacuum is the same as the de Broglie wavelength of an electron, which one is traveling faster through space?
A) The electron because it has more mass.
B) The photon because photons always travel through space faster than electrons.
C) They both have the same speed.

Accepted Answer

Photons always travel at the speed of light in a vacuum, which is the maximum speed anything can travel through space. Electrons, having mass, cannot reach this speed.

Question 12

If the maximum possible accuracy in measuring the position of a particle increases, the maximum possible accuracy in measuring its velocity will
A) increase.
B) decrease.
C) not be affected.

Accepted Answer

According to the Heisenberg Uncertainty Principle, increasing the accuracy in measuring the position of a particle leads to a decrease in the accuracy with which its velocity can be measured. This principle states that the more precisely the position of some particle is determined, the less precisely its momentum (and hence velocity, since velocity is part of momentum) can be known, and vice versa.

Question 13

Monochromatic light is incident on a metal surface, and the ejected electrons give rise to a current in the circuit shown in the figure. The maximum kinetic energy of the ejected electrons is determined by applying a reverse ('stopping') potential, sufficient to reduce the current in the ammeter to zero. If the intensity of the incident light is increased, how will the required stopping potential change? 
A) It will remain unchanged.
B) It will increase.
C) It will decrease.

Accepted Answer

The answer of Monochromatic light is incident on a metal...

Question 14

A beam of light falling on a metal surface is causing electrons to be ejected from the surface. If we now double the frequency of the light, which of the following statements are correct? (There could be more than one correct choice.)
A) The kinetic energy of the ejected electrons doubles.
B) The speed of the ejected electrons doubles.
C) The number of electrons ejected per second doubles.
D) Twice as many photons hit the metal surface as before.
E) None of the above things occur.

Accepted Answer

The answer of A beam of light falling on a...

Question 15

A proton and an electron are both accelerated to the same final kinetic energy. If λ_p is the de Broglie wavelength of the proton and λ_e is the de Broglie wavelength of the electron, then A) λ_p > λ_e. B) λ_p = λ_e. C) λ_p < λ_e.

Accepted Answer

The de Broglie wavelength, λ, is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. For the same kinetic energy, a lighter particle (like an electron) will have a higher velocity and hence a higher momentum than a heavier particle (like a proton), leading to a shorter de Broglie wavelength for the proton compared to the electron.

Question 16

Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes of the crystal surface. What is the wavelength of the x-rays?
A) 0.14 nm
B) 0.17 nm
C) 0.21 nm
D) 0.24 nm
E) 0.27 nm

Accepted Answer

The answer of Certain planes of a crystal of halite...

Question 17

A researcher is using x-rays to investigating a cubic crystal. He is looking at Bragg reflection from the planes parallel to the cube faces. He finds that when using x-rays with a wavelength of 0.165 nm, a strong first maximum occurs when the beam makes an angle of 23.5° with the planes. What is the spacing of adjacent atoms in this crystal?

Accepted Answer

The answer of A researcher is using x-rays to investigating...

Question 18

If the maximum possible accuracy in measuring the velocity of a particle increases, the maximum possible accuracy in measuring its position will
A) increase.
B) decrease.
C) not be affected.

Accepted Answer

This is in accordance with Heisenberg's uncertainty principle, which states that there is a fundamental limit to how precisely both the position and momentum of a particle can be known simultaneously. When the accuracy in measuring the velocity of a particle increases, the accuracy in measuring its momentum also increases, which in turn decreases the maximum possible accuracy in measuring its position. Therefore, option B is the correct answer.

Question 19

A proton and an electron are both accelerated to the same final speed. If λ_p is the de Broglie wavelength of the proton and λ_e is the de Broglie wavelength of the electron, then A) λ_p > λ_e. B) λ_p = λ_e. C) λ_p < λ_e.

Accepted Answer

The de Broglie wavelength is inversely proportional to the momentum of the particle. Since the proton is more massive than the electron, it will have a larger momentum for the same velocity. Therefore, λ_p will be smaller than λ_e.

Question 20

Two sources emit beams of light of wavelength 550 nm. The light from source A has an intensity of 10 µW/m², and the light from source B has an intensity of 20 µW/m². This is all we know about the two beams. Which of the following statements about these beams are correct? (There could be more than one correct choice.) A) Beam B carries twice as many photons per second as beam A. B) A photon in beam B has twice the energy of a photon in beam A. C) The frequency of the light in beam B is twice as great as the frequency of the light in beam A. D) A photon in beam B has the same energy as a photon in beam A. E) None of the above statements are true.

Accepted Answer

Intensity is proportional to the number of photons emitted per unit time per unit area. 
Let the number of photons emitted per second by A be N_A and that by B be N_B. 
Then, 
10 µW/m² = N_A * hc/λ 
20 µW/m² = N_B * hc/λ 
Dividing the second equation by the first, we get: 
2 = N_B/N_A 
So, beam B carries twice as many photons per second as beam A (Option A is correct).

Energy of a photon is given by E = hc/λ. 
Since the wavelength of both beams is the same, the energy per photon is also the same for both beams. So, Option B and D are incorrect.

Frequency is given by f = c/λ, where c is the speed of light. 
Since the wavelength of both beams is the same, the frequency is also the same for both beams. So, Option C is incorrect.

Therefore, the only correct statement is Option A.

Quiz 28: Quantum Physics

Protons are being accelerated in a particle accelerator. When the speed of the protons is doubled, their de Broglie wavelength will

Monochromatic light falls on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons?

When the surface of a metal is exposed to blue light, electrons are emitted. If the intensity of the blue light is increased, which of the following things will also increase?

If a proton and an electron have the same de Broglie wavelengths, which one is moving faster?

A blue laser beam is incident on a metallic surface, causing electrons to be ejected from the metal. If the frequency of the laser beam is increased while the intensity of the beam is held fixed,

If a proton and an electron have the same speed, which one has the longer de Broglie wavelength?

Which of the following actions will increase the de Broglie wavelength of a speck of dust? (There could be more than one correct choice.)

Protons are being accelerated in a particle accelerator. When the energy of the protons is doubled, their de Broglie wavelength will

Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal you should

If the wavelength of a photon in vacuum is the same as the de Broglie wavelength of an electron, which one is traveling faster through space?

If the maximum possible accuracy in measuring the position of a particle increases, the maximum possible accuracy in measuring its velocity will

A beam of light falling on a metal surface is causing electrons to be ejected from the surface. If we now double the frequency of the light, which of the following statements are correct? (There could be more than one correct choice.)

A proton and an electron are both accelerated to the same final kinetic energy. If λp is the de Broglie wavelength of the proton and λe is the de Broglie wavelength of the electron, then

Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes of the crystal surface. What is the wavelength of the x-rays?

If the maximum possible accuracy in measuring the velocity of a particle increases, the maximum possible accuracy in measuring its position will

A proton and an electron are both accelerated to the same final speed. If λp is the de Broglie wavelength of the proton and λe is the de Broglie wavelength of the electron, then

A proton and an electron are both accelerated to the same final kinetic energy. If λ_p is the de Broglie wavelength of the proton and λ_e is the de Broglie wavelength of the electron, then

A proton and an electron are both accelerated to the same final speed. If λ_p is the de Broglie wavelength of the proton and λ_e is the de Broglie wavelength of the electron, then