Question 1

The de Broglie wavelength of an electron (m = 9.11 × 10^-³¹ kg)is 1.2 × 10^-¹⁰ m.Determine the kinetic energy of the electron.

Accepted Answer

The answer of The de Broglie wavelength of an electron...

Question 2

Which one of the following is demonstrated by the Compton effect?

Accepted Answer

The Compton effect demonstrates the particle properties of electromagnetic radiation, as it shows that photons (particles of light) can collide with electrons and transfer some of their energy, causing a change in the wavelength and direction of the photon.

Question 3

A physicist wishes to produce electrons by shining light on a metal surface.The light source emits light with a wavelength of 450 nm.The table lists the only available metals and their work functions.
 
-Which metal(s)can be used to produce electrons by the photoelectric effect?

Accepted Answer

Barium and lithium can be used to produce electrons by the photoelectric effect because they have relatively low work functions, making it easier for photons to eject electrons.

Question 4

A photon has a collision with a stationary electron (h/mc = 2.43 × 10^-¹² m)and loses 5.0% of its energy.The photon scattering angle is 180°.What is the wavelength of the incident photon in this scattering process?

Accepted Answer

The Compton wavelength shift formula is used: Δλ = h/mc (1 - cos θ). For θ = 180°, Δλ = 2h/mc. The energy loss of 5% implies a wavelength increase of 5%, leading to the calculation of the initial wavelength.

Question 5

What kinetic energy must each neutron in a beam of neutrons have if each has a wavelength of 0.10 nm? The mass of a neutron is 1.67 × 10^-²⁷ kg.

Accepted Answer

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Question 6

A physicist wishes to produce electrons by shining light on a metal surface.The light source emits light with a wavelength of 450 nm.The table lists the only available metals and their work functions.
 
-Which entry in the table below correctly identifies the metal that will produce the most energetic electrons and their energies?

Accepted Answer

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Question 7

What is the de Broglie wavelength of an electron (m = 9.11 × 10^-³¹ kg)in a 2.5 × 10³-volt X-ray tube?

Accepted Answer

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Question 8

A photon of wavelength 200 nm is scattered by an electron that is initially at rest.Which one of the following statements concerning the wavelength of the scattered photon is true?

Accepted Answer

When a photon is scattered by an electron (Compton scattering), the wavelength of the scattered photon increases due to the transfer of energy from the photon to the electron. This means the scattered photon's wavelength is greater than the original wavelength.

Question 9

Approximately,what is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 225 V? The mass of an electron is 9.11 × 10^-³¹ kg.

Accepted Answer

The de Broglie wavelength (λ) of an electron can be calculated using the following formula:

λ = h / p

where h is the Planck's constant and p is the momentum of the electron.

The momentum of the electron can be calculated using the following formula:

p = √(2mE)

where m is the mass of the electron, E is the potential difference through which it has been accelerated.

Substituting the given values,

p = √(2 x 9.11 x 10^-31 kg x 225 V)

p = 5.72 x 10^-23 kg m/s

Substituting this value of momentum,

λ = h / p

λ = 6.63 x 10^-34 J s / (5.72 x 10^-23 kg m/s)

λ = 1.16 x 10^-10 m

λ = 0.116 nm

Therefore, the best answer choice is B, which is the closest to the calculated value.

Question 10

Complete the following statement: The photon or "particle" theory of electromagnetic radiation is necessary to explain the

Accepted Answer

The photon theory of electromagnetic radiation was established to explain the results of Compton scattering experiments, where a photon collides with a stationary electron and loses some of its energy as it scatters off in a new direction. This could not be explained by classical wave theory, which predicted that the photon's energy should be distributed evenly in all directions.

Question 11

In the Compton effect,a photon of wavelength  and frequency f hits an electron that is initially at rest.Which one of the following occurs as a result of the collision?

Accepted Answer

In the Compton effect, a photon collides with a stationary electron and transfers some of its energy to the electron, causing the photon's frequency to decrease (losing energy) and its wavelength to increase (wavelength increases as frequency decreases). Therefore, the final photon has a frequency less than f, and its wavelength will also be greater than the original 11ec9e00_fe61_49c7_8d20_b73bf57c2b5e_TB6393_11. Choice D is the only option that reflects these changes.

Question 12

Determine the de Broglie wavelength of a neutron (m = 1.67 × 10^-²⁷ kg)that has a speed of 5.0 m/s.

Accepted Answer

The de Broglie wavelength is given by the equation λ = h/p, where h is Planck's constant and p is the momentum of the particle. The momentum of the neutron is p = mv, where m is the mass of the neutron and v is its speed. Substituting these values into the equation for the de Broglie wavelength, we get:λ = h/p = h/mv = (6.626 × 10^-34 J s)/(1.67 × 10^-27 kg × 5.0 m/s) = 79 nmTherefore, the de Broglie wavelength of the neutron is 79 nm, which corresponds to choice A.

Question 13

The work function for a particular metal is 4.0 eV.Which one of the following best describes the wavelength of electromagnetic radiation needed to eject electrons from this metal?

Accepted Answer

The work function is the minimum energy needed to eject an electron from the metal. To find the wavelength corresponding to this energy, we use the equation $E = \frac{hc}{\lambda}$, where $E$ is the energy in electron volts (eV), $h$ is Planck's constant ($4.135667696 \times 10^{-15}$ eV·s), $c$ is the speed of light ($3 \times 10^8$ m/s), and $\lambda$ is the wavelength in meters. Solving for $\lambda$ gives a value smaller than 310 nm, meaning electromagnetic radiation with a wavelength smaller than 310 nm is needed to provide the energy of 4.0 eV or greater to eject electrons.

Question 14

Which experimental evidence confirms the hypothesis that matter exhibits wave properties?

Accepted Answer

Electron diffraction experiments demonstrate that electrons can exhibit wave-like behavior, confirming the wave properties of matter.

Question 15

Complete the following statement: According to the de Broglie relation,the wavelength of a "matter" wave is inversely proportional to

Accepted Answer

According to de Broglie relation, the wavelength of a "matter" wave is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. Thus, the wavelength is inversely proportional to the momentum of the particle, and hence, the correct choice is C. The other options, i.e., A, B, D, and E, are not relevant to the de Broglie relation.

Question 16

In the Compton scattering experiment shown in the figure,a monochromatic beam of X-rays strikes a target containing free electrons.Scattered X-rays are detected with a wavelength of 2.50 × 10^-¹² m at an angle of 45° away from the original beam direction.What is the wavelength of the incident monochromatic X-rays? Note: The mass of an electron is 9.11 × 10^-³¹ kg.

Accepted Answer

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Question 17

A digital wireless telephone communicates to a base via microwaves with a frequency of 1930 MHz.What are the momentum and energy for the microwave photons emitted by the telephone?

Accepted Answer

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Question 18

Photons of energy 5.0 eV strike a metal surface that has a work function of 3.5 eV.Determine which one of the following best describes the kinetic energy of the emitted electrons.

Accepted Answer

The kinetic energy of the emitted electrons is calculated by subtracting the work function from the photon energy: 5.0 eV - 3.5 eV = 1.5 eV. Therefore, the kinetic energy of the emitted electrons is 1.5 eV or less.

Question 19

What is the speed of an electron that has the same momentum as a photon with a wavelength in vacuum of 488 nm? The mass of an electron is 9.11 × 10^-³¹ kg.

Accepted Answer

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Question 20

Incident X-rays in a Compton scattering experiment have a wavelength of 0.400 nm.Determine the wavelength of the scattered X-rays that are detected at an angle of 80.0°.The Compton wavelength of the electron is 2.43 × 10^-¹² m.

Accepted Answer

The wavelength of the scattered X-rays can be calculated using the Compton scattering formula: $\lambda' = \lambda + h/m_ec \cdot (1 - \cos \theta)$, where $\lambda'$ is the wavelength of the scattered X-rays, $\lambda$ is the initial wavelength (0.400 nm), $h/m_ec$ is the Compton wavelength of the electron (2.43 × 10^-12 m), and $\theta$ is the scattering angle (80.0°). Converting $\lambda$ to meters (0.400 nm = 4.00 × 10^-10 m) and using $\cos(80.0°)$, the calculation yields a new wavelength $\lambda'$ slightly larger than the initial wavelength, which corresponds to option D, 0.402 nm.

Quiz 29: Particles and Waves

The de Broglie wavelength of an electron (m = 9.11 × 10^-³¹ kg) is 1.2 × 10^-¹⁰ m.Determine the kinetic energy of the electron.

Which one of the following is demonstrated by the Compton effect?

A physicist wishes to produce electrons by shining light on a metal surface.The light source emits light with a wavelength of 450 nm.The table lists the only available metals and their work functions. -Which metal(s) can be used to produce electrons by the photoelectric effect?

A photon has a collision with a stationary electron (h/mc = 2.43 × 10^-¹² m) and loses 5.0% of its energy.The photon scattering angle is 180°.What is the wavelength of the incident photon in this scattering process?

What kinetic energy must each neutron in a beam of neutrons have if each has a wavelength of 0.10 nm? The mass of a neutron is 1.67 × 10^-²⁷ kg.

What is the de Broglie wavelength of an electron (m = 9.11 × 10^-³¹ kg) in a 2.5 × 10³-volt X-ray tube?

A photon of wavelength 200 nm is scattered by an electron that is initially at rest.Which one of the following statements concerning the wavelength of the scattered photon is true?

Approximately,what is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 225 V? The mass of an electron is 9.11 × 10^-³¹ kg.

Complete the following statement: The photon or "particle" theory of electromagnetic radiation is necessary to explain the

In the Compton effect,a photon of wavelength and frequency f hits an electron that is initially at rest.Which one of the following occurs as a result of the collision?

Determine the de Broglie wavelength of a neutron (m = 1.67 × 10^-²⁷ kg) that has a speed of 5.0 m/s.

The work function for a particular metal is 4.0 eV.Which one of the following best describes the wavelength of electromagnetic radiation needed to eject electrons from this metal?

Which experimental evidence confirms the hypothesis that matter exhibits wave properties?

Complete the following statement: According to the de Broglie relation,the wavelength of a "matter" wave is inversely proportional to

A digital wireless telephone communicates to a base via microwaves with a frequency of 1930 MHz.What are the momentum and energy for the microwave photons emitted by the telephone?

Photons of energy 5.0 eV strike a metal surface that has a work function of 3.5 eV.Determine which one of the following best describes the kinetic energy of the emitted electrons.

What is the speed of an electron that has the same momentum as a photon with a wavelength in vacuum of 488 nm? The mass of an electron is 9.11 × 10^-³¹ kg.

Incident X-rays in a Compton scattering experiment have a wavelength of 0.400 nm.Determine the wavelength of the scattered X-rays that are detected at an angle of 80.0°.The Compton wavelength of the electron is 2.43 × 10^-¹² m.

Quiz 29: Particles and Waves

The de Broglie wavelength of an electron (m = 9.11 × 10-³¹ kg) is 1.2 × 10-¹⁰ m.Determine the kinetic energy of the electron.

Which one of the following is demonstrated by the Compton effect?

A physicist wishes to produce electrons by shining light on a metal surface.The light source emits light with a wavelength of 450 nm.The table lists the only available metals and their work functions. -Which metal(s) can be used to produce electrons by the photoelectric effect?

A photon has a collision with a stationary electron (h/mc = 2.43 × 10-¹² m) and loses 5.0% of its energy.The photon scattering angle is 180°.What is the wavelength of the incident photon in this scattering process?

What kinetic energy must each neutron in a beam of neutrons have if each has a wavelength of 0.10 nm? The mass of a neutron is 1.67 × 10-²⁷ kg.

What is the de Broglie wavelength of an electron (m = 9.11 × 10-³¹ kg) in a 2.5 × 10³-volt X-ray tube?

A photon of wavelength 200 nm is scattered by an electron that is initially at rest.Which one of the following statements concerning the wavelength of the scattered photon is true?

Approximately,what is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 225 V? The mass of an electron is 9.11 × 10-³¹ kg.

Complete the following statement: The photon or "particle" theory of electromagnetic radiation is necessary to explain the

In the Compton effect,a photon of wavelength and frequency f hits an electron that is initially at rest.Which one of the following occurs as a result of the collision?

Determine the de Broglie wavelength of a neutron (m = 1.67 × 10-²⁷ kg) that has a speed of 5.0 m/s.

The work function for a particular metal is 4.0 eV.Which one of the following best describes the wavelength of electromagnetic radiation needed to eject electrons from this metal?

Which experimental evidence confirms the hypothesis that matter exhibits wave properties?

Complete the following statement: According to the de Broglie relation,the wavelength of a "matter" wave is inversely proportional to

A digital wireless telephone communicates to a base via microwaves with a frequency of 1930 MHz.What are the momentum and energy for the microwave photons emitted by the telephone?

Photons of energy 5.0 eV strike a metal surface that has a work function of 3.5 eV.Determine which one of the following best describes the kinetic energy of the emitted electrons.

What is the speed of an electron that has the same momentum as a photon with a wavelength in vacuum of 488 nm? The mass of an electron is 9.11 × 10-³¹ kg.

Incident X-rays in a Compton scattering experiment have a wavelength of 0.400 nm.Determine the wavelength of the scattered X-rays that are detected at an angle of 80.0°.The Compton wavelength of the electron is 2.43 × 10-¹² m.

The de Broglie wavelength of an electron (m = 9.11 × 10^-³¹ kg) is 1.2 × 10^-¹⁰ m.Determine the kinetic energy of the electron.

A photon has a collision with a stationary electron (h/mc = 2.43 × 10^-¹² m) and loses 5.0% of its energy.The photon scattering angle is 180°.What is the wavelength of the incident photon in this scattering process?

What kinetic energy must each neutron in a beam of neutrons have if each has a wavelength of 0.10 nm? The mass of a neutron is 1.67 × 10^-²⁷ kg.

What is the de Broglie wavelength of an electron (m = 9.11 × 10^-³¹ kg) in a 2.5 × 10³-volt X-ray tube?

Approximately,what is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 225 V? The mass of an electron is 9.11 × 10^-³¹ kg.

Determine the de Broglie wavelength of a neutron (m = 1.67 × 10^-²⁷ kg) that has a speed of 5.0 m/s.

What is the speed of an electron that has the same momentum as a photon with a wavelength in vacuum of 488 nm? The mass of an electron is 9.11 × 10^-³¹ kg.

Incident X-rays in a Compton scattering experiment have a wavelength of 0.400 nm.Determine the wavelength of the scattered X-rays that are detected at an angle of 80.0°.The Compton wavelength of the electron is 2.43 × 10^-¹² m.