Photons from a Laser

solved Photon

Q. Monochromatic light of frequency 6.0 × 10¹⁴ Hz $ν = 6.0 \times 10^{14}$ Hz is produced by a laser. The power emitted is 2.0 × 10⁻³ W $P = 2.0 \times 10^{−3}$ W. How many photons per second, on an average, are emitted by the source?

Inputs

frequency

ν

6e+14 Hz

power

P

0.002 W

Outputs

photons

N

How it's solved

Solved with Photon

Given

$ν = 6.0 \times 10^{14}$ Hz
$P = 2.0 \times 10^{−3}$ W

Find $N$ .

Working

energy of a photon(beam) $E = h \cdot ν$
$E = 6.62607015 \times 10^{−34} \cdot 6 \times 10^{14}$
$E = 3.97564209 \times 10^{−19}$ J
photons carry the power(beam) $P = N \cdot E$
$0.002 = N \cdot 3.97564209 \times 10^{−19}$
$N = 5.031 \times 10^{15}$ s⁻¹
$N \approx 5.0 \times 10^{15}$ s⁻¹to 2 significant figures

Conclusion

Each photon carries Planck's constant times the frequency, so a beam's power is a vast number of very small parcels a second.

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 :photons_from_a_laser do4  kind :numerical5  describes "Monochromatic light of frequency %{frequency} is produced by a laser. The power emitted is %{power}. " \6            "%{photons}?"7  given frequency: "6.0e14 Hz"8  given power: "2.0e-3 W"9  asks photons: "How many photons per second, on an average, are emitted by the source"10end

solution.rb

1require_relative "../questions/photons_from_a_laser"2require_relative "../science/dual_nature_of_radiation_and_matter/photon"34solve :photons_from_a_laser, using: Photon do5  objects :beam67  take frequency: beam.frequency8  take power: beam.emitted_power910  photons = beam.photons_a_second11  answer photons:, in: "s-1", figures: 21213  conclusion "Each photon carries Planck's constant times the frequency, so a beam's power is a vast " \14             "number of very small parcels a second."15end

playground.rb

1require_relative "../solutions/photons_from_a_laser"23play_with :photons_from_a_laser do4  title "Photons from a Laser"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)