What is the maximum speed of electrons ejected from the surface of platinum

| September 1, 2021 | education

What is the maximum speed of electrons ejected from the surface of platinum when it is irradiated with light with a wavelength of 100 nm? The work function of electrons from platinum is 5.3 eV.

λ = 100 nm = 100 * 10 ^ -9 m.

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

Av = 5.3 eV = 8.48 * 10 ^ -19 J.

m = 9.1 * 10 ^ -31 kg.

s = 3 * 10 ^ 8 m / s.

V -?

According to the law of conservation of energy, the energy carried by the photon Eph is spent on tearing out the electron from the surface of the metal Av and communicating the kinetic energy Ek to it: Eph = Av + ​​Ek.

The energy of a photon is expressed by the formula: Eph = h * s / λ, where h is Planck’s constant, c is the speed of light, λ is the wavelength of the photon.

The kinetic energy of electrons Ek is determined by the formula: Ek = m * V ^ 2/2.

h * c / λ = Av + ​​m * V ^ 2/2.

m * V ^ 2/2 = h * s / λ – Av.

V = √ (2 * (h * s / λ – Av) / m).

Av = 5.3 eV = 5.3 * 1.6 * 10 ^ -19 J = 8.48 10 ^ -19 J.

V = √ (2 * (6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s / 100 * 10 ^ -9 m – 8.48 * 10 ^ -19 J) / 9, 1 * 10 ^ -31 kg = 1.6 * 10 ^ 6 m / s.

Answer: electrons fly out of the plate at a speed of V = 1.6 * 10 ^ 6 m / s.



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