At what frequency of light incident on the surface of a metal body with a work function of 2.2 eV

| June 12, 2021 | education

At what frequency of light incident on the surface of a metal body with a work function of 2.2 eV, the maximum photoelectron speed is 1000 km / s?

Av = 2.2 eV = 3.52 * 10 ^ -19 J.

Vmax = 1000 km / s = 1 * 10 ^ 6 m / s.

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

m = 9.1 * 10 ^ -31 kg.

C = 3 * 10 ^ 8 m / s.

v -?

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

Eph = Av + ​​Ek – the law of the photoelectric effect.

The energy of photons Eph is expressed by the formula: Eph = h * v, where h is Planck’s constant, v is the frequency of the incident photons.

We express the kinetic energy of the outgoing electrons Ek by the formula: Ek = m * V ^ 2/2, where m is the mass of the electron, V is the velocity of the electron escaping from the metal surface.

h * v = Av + ​​m * Vmax2 / 2.

The photon frequency v will be determined by the formula: v = Av / h + m * Vmax ^ 2/2 * h.

v = 3.52 * 10 ^ -19 J / 6.6 * 10 ^ -34 J * s + 9.1 * 10 ^ -31 kg * (1 * 10 ^ 6 m / s) ^ 2/2 * 6 , 6 * 10 ^ -34 J * s = 1.22 * 10 ^ 15 Hz.

Answer: the incident light has a frequency of v = 1.22 * 10 ^ 15 Hz.



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