A Helium-Neon Photon's Momentum

solved Photon

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?

Inputs

wavelength

λ

632.8 nm

Outputs

momentum

p

How it's solved

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 web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

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

solution.rb

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

playground.rb

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 it drew on

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)