A Helium-Neon Laser's Photons

solved Photon

Q. Monochromatic light of wavelength 632.8 nm $λ = 632.8$ nm is produced by a helium-neon laser. What is the energy of each photon in the light beam, in J?

Inputs

wavelength

λ

632.8 nm

Outputs

energy

E

How it's solved

Solved with Photon

Given

$λ = 632.8$ nm

Find $E$ .

Working

$λ = 632.8$ nm $= 6.328 \times 10^{−7}$ m
frequency and wavelength of light(beam) $c = ν \cdot λ$
$2.99792458 \times 10^{8} = ν \cdot 6.328 \times 10^{−7}$
$ν = 4.73755465 \times 10^{14}$ Hz
energy of a photon(beam) $E = h \cdot ν$
$E = 6.62607015 \times 10^{−34} \cdot 4.73755465 \times 10^{14}$
$E = 3.139 \times 10^{−19}$ J
$E \approx 3.14 \times 10^{−19}$ Jto 3 significant figures

Conclusion

A photon's energy is Planck's constant times its frequency, and the frequency is the speed of light over the wavelength.

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_laser_s_photons do4  kind :numerical5  describes "Monochromatic light of wavelength %{wavelength} is produced by a helium-neon laser. %{energy}, in J?"6  given wavelength: "632.8 nm"7  asks energy: "What is the energy of each photon in the light beam"8end

solution.rb

1require_relative "../questions/a_helium_neon_laser_s_photons"2require_relative "../science/dual_nature_of_radiation_and_matter/photon"34solve :a_helium_neon_laser_s_photons, using: Photon do5  objects :beam67  take wavelength: beam.wavelength89  energy = beam.photon_energy10  answer energy:, in: "J", figures: 31112  conclusion "A photon's energy is Planck's constant times its frequency, and the frequency is the speed of light " \13             "over the wavelength."14end

playground.rb

1require_relative "../solutions/a_helium_neon_laser_s_photons"23play_with :a_helium_neon_laser_s_photons do4  title "A Helium-Neon Laser's Photons"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)