Caesium Stopped at 0.60 V

Q. The work function of caesium is 2.14 eV. What is the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of 0.60 V, in nm? expects 452 nm

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Q. The work function of caesium is 2.14 eV $φ_{0} = 2.14$ eV. What is the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of 0.60 V $V_{0} = 0.60$ V, in nm?

The playground

Inputs

work function

φ_{0}

2.14 eV

stopping

V_{0}

0.6 V

Outputs

wavelength

λ

The solution

Solved with PhotoelectricEffect

Given

$φ_{0} = 2.14$ eV
$V_{0} = 0.60$ V

Find $λ$ .

Working

$φ_{0} = 2.14$ eV $= 3.428658 \times 10^{−19}$ J
einsteins photoelectric equation(caesium) $e \cdot V_{0} = h \cdot ν - φ_{0}$
$1.60217663 \times 10^{−19} \cdot 0.6 = 6.62607015 \times 10^{−34} \cdot ν - 3.428658 \times 10^{−19}$
$ν = 6.62529052 \times 10^{14}$ Hz
frequency and wavelength of light(caesium) $c = ν \cdot λ$
$2.99792458 \times 10^{8} = 6.62529052 \times 10^{14} \cdot λ$
$λ = 452.5$ nm
$λ = 4.52497075 \times 10^{−7}$ m $= 452.497075$ nm
$λ \approx 452$ nmto 3 significant figures

Conclusion

The stopping potential measures the fastest electron's energy; add the work function and you have the photon's energy, and so its wavelength.

The Ruby

1require_relative "../physics"23question :caesium_stopped_at_sixty_centivolts do4  kind :numerical5  describes "The work function of caesium is %{work_function}. %{wavelength} if the photocurrent is brought to zero " \6            "by a stopping potential of %{stopping}, in nm?"7  given work_function: "2.14 eV"8  given stopping: "0.60 V"9  asks wavelength: "What is the wavelength of the incident light"10end

1require_relative "../questions/caesium_stopped_at_sixty_centivolts"2require_relative "../science/dual_nature_of_radiation_and_matter/photoelectric_effect"34solve :caesium_stopped_at_sixty_centivolts, using: PhotoelectricEffect do5  objects :caesium67  take work_function: caesium.work_function8  take stopping: caesium.stopping_potential910  wavelength = caesium.wavelength11  answer wavelength:, in: "nm", figures: 31213  conclusion "The stopping potential measures the fastest electron's energy; add the work function and you have " \14             "the photon's energy, and so its wavelength."15end

1require_relative "../solutions/caesium_stopped_at_sixty_centivolts"23play_with :caesium_stopped_at_sixty_centivolts do4  title "Caesium Stopped at 0.60 V"5end

The laws

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 caesium	$ν$	Hz	0 … ∞
wavelength of caesium	$λ$	m	0 … ∞
threshold frequency of ground	$ν_{0,g}$	Hz	—
work function of ground	$φ_{0,g}$	J	—
threshold frequency of caesium	$ν_{0}$	Hz	—
work function of caesium	$φ_{0}$	J	—
stopping potential of ground	$V_{0,g}$	V	—
stopping potential of caesium	$V_{0}$	V	—
maximum kinetic energy of ground	$K_{max,g}$	J	—
maximum kinetic energy of caesium	$K_{\max}$	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(caesium)

h \cdot ν_{0,g} = φ_{0,g}

threshold of emission(ground)

h \cdot ν_{0} = φ_{0}

threshold of emission(caesium)

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(caesium)

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(caesium)