A Helium-Neon Photon's Momentum

Q. Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. What is the momentum of each photon in the light beam, in kg m/s? expects 1.05 × 10⁻²⁷ kg m/s

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Q. Monochromatic light of wavelength 632.8 nm $λ = 632.8$ nm is produced by a helium-neon laser. What is the momentum of each photon in the light beam, in kg m/s?

The playground

Inputs

wavelength

λ

632.8 nm

Outputs

momentum

p

The solution

Solved with Photon

Given

$λ = 632.8$ nm

Find $p$ .

Working

$λ = 632.8$ nm $= 6.328 \times 10^{−7}$ m
momentum of a photon(beam) $p = \frac{h}{λ}$
$p = \frac{6.62607015 \times 10^{−34}}{6.328 \times 10^{−7}}$
$p = 1.047 \times 10^{−27}$ kg m/s
$p \approx 1.05 \times 10^{−27}$ kg m/sto 3 significant figures

Conclusion

A photon carries momentum of Planck's constant over its wavelength, tiny for visible light.

The Ruby

1require_relative "../physics"23question :a_helium_neon_photon_s_momentum do4  kind :numerical5  describes "Monochromatic light of wavelength %{wavelength} is produced by a helium-neon laser. %{momentum}, in " \6            "kg m/s?"7  given wavelength: "632.8 nm"8  asks momentum: "What is the momentum of each photon in the light beam"9end

1require_relative "../questions/a_helium_neon_photon_s_momentum"2require_relative "../science/dual_nature_of_radiation_and_matter/photon"34solve :a_helium_neon_photon_s_momentum, using: Photon do5  objects :beam67  take wavelength: beam.wavelength89  momentum = beam.photon_momentum10  answer momentum:, in: "kg m/s", figures: 31112  conclusion "A photon carries momentum of Planck's constant over its wavelength, tiny for visible light."13end

1require_relative "../solutions/a_helium_neon_photon_s_momentum"23play_with :a_helium_neon_photon_s_momentum do4  title "A Helium-Neon Photon's Momentum"5end

The laws

quantity	written	units	within	from
plancks constant	$h$	J s	—	Photon
speed of light	$c$	m/s	—	Photon
elementary charge	$e$	C	—	Photon
frequency	$ν$	Hz	0 … ∞	Photon
wavelength	$λ$	m	0 … ∞	Photon
photon energy	$E$	J	—	Photon
photon momentum	$p$	kg m/s	—	Photon
emitted power	$P$	W	—	Photon
photons a second	$N$	s⁻¹	—	Photon
accelerating potential	$V$	V	—	Photon
photon energy of ground	$E_{g}$	J	—
frequency of ground	$ν_{g}$	Hz	0 … ∞
photon energy of beam	$E$	J	—
frequency of beam	$ν$	Hz	0 … ∞
wavelength of ground	$λ_{g}$	m	0 … ∞
wavelength of beam	$λ$	m	0 … ∞
photon momentum of ground	$p_{g}$	kg m/s	—
photon momentum of beam	$p$	kg m/s	—
emitted power of ground	$P_{g}$	W	—
photons a second of ground	$N_{g}$	s⁻¹	—
emitted power of beam	$P$	W	—
photons a second of beam	$N$	s⁻¹	—
accelerating potential of beam	$V$	V	—

E_{l} = h \cdot ν_{l}

energy of a photon

c = ν_{l} \cdot λ_{l}

frequency and wavelength of light

p_{l} = \frac{h}{λ_{l}}

momentum of a photon

P_{l} = N_{l} \cdot E_{l}

photons carry the power

E_{g} = h \cdot ν_{g}

energy of a photon(ground)

E = h \cdot ν

energy of a photon(beam)

c = ν_{g} \cdot λ_{g}

frequency and wavelength of light(ground)

c = ν \cdot λ

frequency and wavelength of light(beam)

p_{g} = \frac{h}{λ_{g}}

momentum of a photon(ground)

p = \frac{h}{λ}

momentum of a photon(beam)

P_{g} = N_{g} \cdot E_{g}

photons carry the power(ground)

P = N \cdot E

photons carry the power(beam)