# 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.