Question 1

A light-emitting diode emits one microwatt of 640 nm photons. How many photons are emitted each second?

Accepted Answer

The energy of one photon is given by E = hc/λ, where h is Planck's constant (6.626 × 10^-34 J·s), c is the speed of light (3 × 10^8 m/s), and λ is the wavelength (640 nm = 640 × 10^-9 m). Calculate the energy per photon and divide the total power (1 microwatt = 1 × 10^-6 W) by this energy to find the number of photons emitted per second.

Question 2

In a particular case of Compton scattering, a photon collides with a free electron and scatters backwards. The wavelength after the collision is exactly double the wavelength before the collision. What is the wavelength of the incident photon?

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Question 3

What is the momentum of a photon of light that has a frequency of 2.8 × 10¹⁴ Hz?

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Question 4

What is the number of photons per second given off by a light bulb with a power of 100 Watts operating at an efficiency of 4.80%? Assume the wavelength of light to be 600 nm.

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Question 5

A beam of white light of a certain frequency is incident on a metal surface. If the work function of this surface is 2.20 eV, what frequency of light would give a maximum kinetic energy of 0.25 eV to the photoelectrons ejected from this surface?

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Question 6

A photon of wavelength 1.50 × 10^-10 m is scattered at an angle of 90° in the Compton effect. The wavelength of the scattered photon is

Accepted Answer

The Compton wavelength shift formula is Δλ = (h/mc)(1 - cos θ). For θ = 90°, Δλ = h/mc. Using h/mc ≈ 2.43 × 10^-12 m, the new wavelength is 1.50 × 10^-10 m + 2.43 × 10^-12 m = 1.52 × 10^-10 m.

Question 7

A surface has a work function 1.70 eV and has light of wavelength 400 nm shone on it. What is the maximum speed of the photoelectrons emitted?

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Question 8

What is the longest wavelength of light that can cause photoelectron emission from a metal that has a work function of 2.20 eV?

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Question 9

What is the cutoff frequency for a metal surface that has a work function of 5.42 eV?

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Question 10

A surface has a work function 1.70 eV and has light of wavelength 400 nm shone on it. What is the kinetic energy of the photoelectrons emitted?

Accepted Answer

The energy of the incident photons is calculated using the formula E = hc/λ, where h is Planck's constant (4.135667696 x 10^-15 eV·s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength (400 nm = 400 x 10^-9 m). This gives E ≈ 3.11 eV. The kinetic energy of the emitted photoelectrons is the photon energy minus the work function: KE = 3.11 eV - 1.70 eV = 1.41 eV.

Question 11

A 60-W bulb is operating at an efficiency of 6.20%. What is the number of photons per second given off by the bulb assuming the wavelength of light to be 580 nm?

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Question 12

A photon has an energy of 6.60 eV. To what wavelength does this energy correspond?

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Question 13

A beam of light with a frequency range of 3.01 × 10¹⁴ Hz - 6.10 × 10¹⁴ Hz is incident on a metal surface. If the work function of the metal surface is 2.20 eV, what is the range of frequencies in this beam of light that will be responsible for ejecting electrons from this metal surface?

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Question 14

A beam of light with a frequency range of 3.01 × 10¹⁴ Hz - 6.10 × 10¹⁴ Hz is incident on a metal surface. If the work function of the metal surface is 2.20 eV, what is the maximum kinetic energy of photoelectrons ejected from this surface?

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Question 15

Electrons are emitted from a surface when light of wavelength 500 nm is shone on the surface but electrons are not emitted for longer wavelengths of light. The work function of the surface is

Accepted Answer

The work function is the minimum energy needed to emit electrons from a surface. Using the equation $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength, we find the energy for 500 nm light is approximately 2.5 eV. This is the work function since longer wavelengths (lower energy) do not emit electrons.

Question 16

Light with a frequency of 8.70 × 10¹⁴ Hz is incident on a metal that has a work function of 2.8 eV. What is the maximum kinetic energy that a photoelectron ejected in this process can have?

Accepted Answer

The maximum kinetic energy of a photoelectron is given by the equation:KE = hf - Φwhere h is Planck's constant, f is the frequency of the light, and Φ is the work function of the metal.Plugging in the given values, we get:KE = (6.626 × 10^-34 J s)(8.70 × 10^14 Hz) - (2.8 eV)(1.602 × 10^-19 J/eV)KE = 1.28 × 10^-19 JTherefore, the maximum kinetic energy that a photoelectron ejected in this process can have is 1.28 × 10^-19 J.

Question 17

Light with a wavelength of 310 nm is incident on a metal that has a work function of 3.8 eV. What is the maximum kinetic energy that a photoelectron ejected in this process can have?

Accepted Answer

The maximum kinetic energy of a photoelectron can be found using the following equation:

KE=max(0,Ephoton - Work function)

where KE is the kinetic energy of the photoelectron, Ephoton is the energy of the incident photon, and the work function is the minimum amount of energy needed to remove an electron from the metal.

We are given the wavelength of the incident light, but we need to convert it to energy:

Ephoton = hc/λ

where h is Planck's constant, c is the speed of light, and λ is the wavelength.

Plugging in our given values:

Ephoton = hc/λ = (6.626 × 10^-34 J*s)(2.998 × 10^8 m/s)/(310 × 10^-9 m) = 6.393 × 10^-19 J

Now we can use the above equation to find the maximum kinetic energy:

KE=max(0,Ephoton - Work function) = max(0,6.393 × 10^-19 J - 3.8 eV)

Converting the work function to joules:

3.8 eV = 3.8 × 1.602 × 10^-19 J/eV = 6.0856 × 10^-19 J

Plugging in the values:

KE=max(0,6.393 × 10^-19 J - 6.0856 × 10^-19 J) = max(0,3.074 × 10^-20 J)

Therefore, the maximum kinetic energy of the photoelectron is 3.074 × 10^-20 J, which is equivalent to 0.33 × 10^-19 J in scientific notation. The closest answer choice is E, which is the correct answer.

Question 18

The work function of a certain metal is 1.90 eV. What is the longest wavelength of light that can cause photoelectron emission from this metal?

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Question 19

What is the momentum of a photon of light that has a wavelength of 480 nm?

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