Photons from a Laser

Q. Monochromatic light of frequency 6.0 × 10¹⁴ Hz is produced by a laser. The power emitted is 2.0 × 10⁻³ W. How many photons per second, on an average, are emitted by the source? expects 5.0 × 10¹⁵ s⁻¹

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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?

The playground

Inputs

frequency

ν

6e+14 Hz

power

P

0.002 W

Outputs

photons

N

The solution

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 Ruby

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

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

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