The Emitter of an Argon Laser

solved PhotoelectricEffect

Q. Light of wavelength 488 nm $λ = 488$ nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V $V_{0} = 0.38$ V. What is the work function of the material from which the emitter is made, in eV?

Inputs

wavelength

λ

488 nm

stopping

V_{0}

0.38 V

Outputs

work function

φ_{0}

How it's solved

Solved with PhotoelectricEffect

Given

$λ = 488$ nm
$V_{0} = 0.38$ V

Find $φ_{0}$ .

Working

$λ = 488$ nm $= 4.88 \times 10^{−7}$ m
frequency and wavelength of light(emitter) $c = ν \cdot λ$
$2.99792458 \times 10^{8} = ν \cdot 4.88 \times 10^{−7}$
$ν = 6.14328807 \times 10^{14}$ Hz
einsteins photoelectric equation(emitter) $e \cdot V_{0} = h \cdot ν - φ_{0}$
$1.60217663 \times 10^{−19} \cdot 0.38 = 6.62607015 \times 10^{−34} \cdot 6.14328807 \times 10^{14} - φ_{0}$
$φ_{0} = 2.161$ eV
$φ_{0} = 3.46175865 \times 10^{−19}$ J $= 2.1606598$ eV
$φ_{0} \approx 2.16$ eVto 3 significant figures

Conclusion

The photon's energy splits into the work function and the fastest electron's energy, which the stopping potential measures.

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 :the_emitter_of_an_argon_laser do4  kind :numerical5  describes "Light of wavelength %{wavelength} is produced by an argon laser which is used in the photoelectric " \6            "effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) " \7            "potential of photoelectrons is %{stopping}. %{work_function}, in eV?"8  given wavelength: "488 nm"9  given stopping: "0.38 V"10  asks work_function: "What is the work function of the material from which the emitter is made"11end

solution.rb

1require_relative "../questions/the_emitter_of_an_argon_laser"2require_relative "../science/dual_nature_of_radiation_and_matter/photoelectric_effect"34solve :the_emitter_of_an_argon_laser, using: PhotoelectricEffect do5  objects :emitter67  take wavelength: emitter.wavelength8  take stopping: emitter.stopping_potential910  work_function = emitter.work_function11  answer work_function:, in: "eV", figures: 31213  conclusion "The photon's energy splits into the work function and the fastest electron's energy, which the " \14             "stopping potential measures."15end

playground.rb

1require_relative "../solutions/the_emitter_of_an_argon_laser"23play_with :the_emitter_of_an_argon_laser do4  title "The Emitter of an Argon Laser"5end

The laws it drew on

quantity	written	units	within	from
plancks constant	$h$	J s	—	PhotoelectricEffect
elementary charge	$e$	C	—	PhotoelectricEffect
speed of light	$c$	m/s	—	PhotoelectricEffect
frequency	$ν$	Hz	0 … ∞	PhotoelectricEffect
wavelength	$λ$	m	0 … ∞	PhotoelectricEffect
work function	$φ_{0}$	J	—	PhotoelectricEffect
threshold frequency	$ν_{0}$	Hz	—	PhotoelectricEffect
stopping potential	$V_{0}$	V	—	PhotoelectricEffect
maximum kinetic energy	$K_{\max}$	J	—	PhotoelectricEffect
frequency of ground	$ν_{g}$	Hz	0 … ∞
wavelength of ground	$λ_{g}$	m	0 … ∞
frequency of emitter	$ν$	Hz	0 … ∞
wavelength of emitter	$λ$	m	0 … ∞
threshold frequency of ground	$ν_{0,g}$	Hz	—
work function of ground	$φ_{0,g}$	J	—
threshold frequency of emitter	$ν_{0}$	Hz	—
work function of emitter	$φ_{0}$	J	—
stopping potential of ground	$V_{0,g}$	V	—
stopping potential of emitter	$V_{0}$	V	—
maximum kinetic energy of ground	$K_{max,g}$	J	—
maximum kinetic energy of emitter	$K_{\max}$	J	—

c = ν_{l} \cdot λ_{l}

frequency and wavelength of light

h \cdot ν_{0,m} = φ_{0,m}

threshold of emission

e \cdot V_{0,m} = h \cdot ν_{m} - φ_{0,m}

einsteins photoelectric equation

e \cdot V_{0,m} = K_{max,m}

the stopping potential stops the fastest

c = ν_{g} \cdot λ_{g}

frequency and wavelength of light(ground)

c = ν \cdot λ

frequency and wavelength of light(emitter)

h \cdot ν_{0,g} = φ_{0,g}

threshold of emission(ground)

h \cdot ν_{0} = φ_{0}

threshold of emission(emitter)

e \cdot V_{0,g} = h \cdot ν_{g} - φ_{0,g}

einsteins photoelectric equation(ground)

e \cdot V_{0} = h \cdot ν - φ_{0}

einsteins photoelectric equation(emitter)

e \cdot V_{0,g} = K_{max,g}

the stopping potential stops the fastest(ground)

e \cdot V_{0} = K_{\max}

the stopping potential stops the fastest(emitter)