What is the wavelength of the radiation if the maximum speed of the emitted particles of electrons during the photoelectric

| September 20, 2021 | education

What is the wavelength of the radiation if the maximum speed of the emitted particles of electrons during the photoelectric effect is equal to 1.6 * 10 ^ 6 work A = 5.3 m = 9.1 * 10 ^ -31

V = 1.6 * 10 ^ 6 m / s.

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

m = 9.1 * 10 ^ -31 kg.

C = 3 * 10 ^ 8 m / s.

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

λ -?

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

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

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

h * C / λ = Ab + m * V ^ 2/2.

We express the wavelength λ by the formula: λ = h * C / (Av + m * V ^ 2/2).

λ = 6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s / (8.48 * 10 ^ -19 J + 9.1 * 10 ^ -31 kg * (1.6 * 10 ^ 6 m / s) ^ 2/2) = 0.98 * 10 ^ -7 m.

Answer: the wavelength of the glowing radiation is λ = 0.98 * 10 ^ -7 m.



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