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22.1. Energy and momentum of a photon
A subsection of Physics, 9702, through 22. Quantum physics
Listing 10 of 18 questions
Light of wavelength 590 nm is incident normally on a surface, as illustrated in . surface light wavelength 590 nm The power of the light is 3.2 mW. The light is completely absorbed by the surface. Calculate the number of photons incident on the surface in 1.0 s. number = Use your answer in to determine the total momentum of the photons arriving at the surface in 1.0 s, momentum = kg m s−1 the force exerted on the surface by the light. force = N
9702_s14_qp_42
THEORY
2014
Paper 4, Variant 2
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A photon of wavelength 6.50 × 10−12 m is incident on an isolated stationary electron, as illustrated in . incident photon electron mass me deflected photon wavelength 6.84 × 10–12 m e wavelength 6.50 × 10–12 m The photon is deflected elastically by the electron of mass me. The wavelength of the deflected photon is 6.84 × 10−12 m. Calculate, for the incident photon, its momentum, momentum = N s its energy. energy = J The angle θ through which the photon is deflected is given by the expression Δλ = h mec (1 – cos θ) where Δλ is the change in wavelength of the photon, h is the Planck constant and c is the speed of light in free space. Calculate the angle θ. θ = ° Use energy considerations to suggest why Δλ must always be positive.
9702_s15_qp_41
THEORY
2015
Paper 4, Variant 1
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Explain what is meant by a photon. An X-ray photon of energy 3.06 × 10–14 J is incident on an isolated stationary electron, as illustrated in . incident photon deflected photon wavelength 6.80 × 10–12 m e energy 3.06 × 10–14 J The photon is deflected elastically by the electron through angle θ. The deflected photon has a wavelength of 6.80 × 10–12 m. On , draw an arrow to indicate a possible initial direction of motion of the electron after the photon has been deflected. Calculate 1. the energy of the deflected photon, photon energy = J 2. the speed of the electron after the photon has been deflected. speed = m s–1 Explain why the magnitude of the final momentum of the electron is not equal to the change in magnitude of the momentum of the photon.
9702_s15_qp_42
THEORY
2015
Paper 4, Variant 2
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A photon of wavelength 6.50 × 10−12 m is incident on an isolated stationary electron, as illustrated in . incident photon electron mass me deflected photon wavelength 6.84 × 10–12 m e wavelength 6.50 × 10–12 m The photon is deflected elastically by the electron of mass me. The wavelength of the deflected photon is 6.84 × 10−12 m. Calculate, for the incident photon, its momentum, momentum = N s its energy. energy = J The angle θ through which the photon is deflected is given by the expression Δλ = h mec (1 – cos θ) where Δλ is the change in wavelength of the photon, h is the Planck constant and c is the speed of light in free space. Calculate the angle θ. θ = ° Use energy considerations to suggest why Δλ must always be positive.
9702_s15_qp_43
THEORY
2015
Paper 4, Variant 3
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A photon of wavelength 540 nm collides with an isolated stationary electron, as illustrated in . electron incident photon wavelength 540 nm deflected photon wavelength 544 nm The photon is deflected elastically by the electron. The wavelength of the deflected photon is 544 nm. State what is meant by a photon. On , draw an arrow to indicate the approximate direction of motion of the deflected electron. Calculate: the momentum of the deflected photon momentum = N s the energy transferred to the deflected electron. energy = J Another photon of wavelength 540 nm collides with an isolated stationary electron. Explain why it is not possible for the deflected photon to have a wavelength less than 540 nm.
9702_w20_qp_41
THEORY
2020
Paper 4, Variant 1
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A photon of wavelength 540 nm collides with an isolated stationary electron, as illustrated in . electron incident photon wavelength 540 nm deflected photon wavelength 544 nm The photon is deflected elastically by the electron. The wavelength of the deflected photon is 544 nm. State what is meant by a photon. On , draw an arrow to indicate the approximate direction of motion of the deflected electron. Calculate: the momentum of the deflected photon momentum = N s the energy transferred to the deflected electron. energy = J Another photon of wavelength 540 nm collides with an isolated stationary electron. Explain why it is not possible for the deflected photon to have a wavelength less than 540 nm.
9702_w20_qp_43
THEORY
2020
Paper 4, Variant 3
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Show that the momentum p of a photon of electromagnetic radiation with wavelength λ is given by p = h λ where h is the Planck constant. Use the expression in to show that a photon in free space that has a momentum of 9.5 × 10–28 N s is a photon of red light. A beam of red light of intensity 160 W m–2 is incident normally on a plane mirror, as shown in . The momentum of each photon in the beam is 9.5 × 10–28 N s. beam of red light, intensity 160 W m–2 plane mirror All of the light is reflected by the mirror in the opposite direction to its original path. The cross-sectional area of the beam is 2.5 × 10–6 m2. Show that the number of photons incident on the mirror per unit time is 1.4 × 1015 s–1. Use the information in to determine the pressure exerted by the light beam on the mirror. pressure = Pa The beam of red light in is now replaced with a beam of blue light of the same intensity. Suggest and explain whether the pressure exerted on the mirror by the beam of blue light is less than, the same as, or greater than the pressure exerted by the beam of red light.
9702_w23_qp_41
THEORY
2023
Paper 4, Variant 1
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Show that the momentum p of a photon of electromagnetic radiation with wavelength λ is given by p = h λ where h is the Planck constant. Use the expression in to show that a photon in free space that has a momentum of 9.5 × 10–28 N s is a photon of red light. A beam of red light of intensity 160 W m–2 is incident normally on a plane mirror, as shown in . The momentum of each photon in the beam is 9.5 × 10–28 N s. beam of red light, intensity 160 W m–2 plane mirror All of the light is reflected by the mirror in the opposite direction to its original path. The cross-sectional area of the beam is 2.5 × 10–6 m2. Show that the number of photons incident on the mirror per unit time is 1.4 × 1015 s–1. Use the information in to determine the pressure exerted by the light beam on the mirror. pressure = Pa The beam of red light in is now replaced with a beam of blue light of the same intensity. Suggest and explain whether the pressure exerted on the mirror by the beam of blue light is less than, the same as, or greater than the pressure exerted by the beam of red light.
9702_w23_qp_43
THEORY
2023
Paper 4, Variant 3
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Questions Discovered
18