# Determine the wavelength of light (in nm) irradiating a photocathode with a work function

Determine the wavelength of light (in nm) irradiating a photocathode with a work function of A = 3.7 eV, if the maximum kinetic energy of photoelectrons is T max = 1.7 eV.

Av = 3.7 eV = 5.92 * 10 ^ -19 J.

Tmax = 1.7 eV = 2.72 * 10 ^ -19 J.

h = 6.6 * 10 ^ -34 J * s.

C = 3 * 10 ^ 8 m / s.

λ -?

The energy of the incident photons Eph goes to knock out electrons from the surface of the metal AB and impart kinetic energy Tmax to them.

Eph = Av + Tmax.

The energy of photons Eph of light that fall on the photocathode can be expressed by the formula: Ef = h * C / λ, where h is Planck’s constant, C is the speed of light, λ is the wavelength of photons.

h * C / λ = Av + Tmax.

λ = h * C / (Av + Tmax).

λ = 6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s / (5.92 * 10 ^ -19 J + 2.72 * 10 ^ -19 J) = 25.46 * 10 ^ -9 m = 25.46 nm.

Answer: the photocathode is irradiated with a wavelength λ = 25.46 nm.

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