# The work function of electrons from a certain metal is 5.2 × 10−19 J. Photons with a momentum of 2.4

The work function of electrons from a certain metal is 5.2 × 10−19 J. Photons with a momentum of 2.4 × 10−27 kg • m / s are incident on the metal. How many times is the maximum momentum of electrons escaping from the metal surface during the photoelectric effect, greater than the momentum of incident photons?

Av = 5.2 * 10 ^ -19 J.

рф = 2.4 * 10 ^ -27 kg * m / s.

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

me = 9.1 * 10 ^ -31 kg.

s = 3 * 10 ^ 8 m / s.

pe / rf -?

The momentum of the incident photons рф is expressed by the formula: рф = h / λ.

λ = h / рф.

λ = 6.6 * 10 ^ -34 J * s / 2.4 * 10 ^ -27 kg * m / s = 2.75 * 10 ^ -7 m.

The momentum of electrons pe, which fly out of the metal surface, can be expressed by the formula: pe = me * V.

h * s / λ = Av + ​​me * V ^ 2/2 – the law of the photoelectric effect.

me * V ^ 2/2 = h * s / λ – Av.

V ^ 2 = 2 * h * s / me * λ – 2 * Av / me.

V = √ (2 * h * s / m * λ – 2 * Av / m).

V = √ (2 * 6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s / 9.1 * 10 ^ -31 kg * 2.75 * 10 ^ -7 m – 2 * 5 , 2 * 10 ^ -19 J / 9.1 * 10 ^ -31 kg) = 0.66 * 10 ^ 6 m / s.

pe = 9.1 * 10 ^ -31 kg * 0.66 * 10 ^ 6 m / s = 6 * 10 ^ -25 kg * m / s.

pe / rf = 6 * 10 ^ -25 kg * m / s / 2.4 * 10 ^ -27 kg * m / s = 2.5 * 10 ^ 2 = 250.

Answer: the momentum of electrons is 250 times greater than the momentum of photons: pe / pf = 250.

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