# The red border of the photoelectric effect for zinc is 3.1 · 10-7 m. Determine the maximum kinetic energy

**The red border of the photoelectric effect for zinc is 3.1 · 10-7 m. Determine the maximum kinetic energy of photoelectrons if light with a wavelength of 2 · 10-7 m. S = 3 · 108 m / s, h = 6.62 · 10- 34 J s.**

λcr = 3.1 * 10-7 m

λ = 2 * 10-7 m.

h = 6.6 * 10-34 J * s.

C = 3 * 10 ^ 8 m / s.

Ek -?

In order for the phenomenon of the photoeffect to be observed, it is necessary that the energy of the incident photons Eph be sufficient to pull out the electrons Ab from the metal surface and impart kinetic energy Ek to them: Ef = Av + Ek.

Let us express the maximum energy of electron emission by the formula: Ek = Eph – Av.

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

Eph = 6.6 * 10-34 J * s * 3 * 10 ^ 8 m / s / 2 * 10-7 m = 9.9 * 10-19 J.

The work function Av of electrons from the zinc surface is expressed by the formula: Av = h * C / λcr.

Av = 6.6 * 10-34 J * s * 3 * 10 ^ 8 m / s / 3.1 * 10-7 m = 6.3 * 10-19 J.

Ek = 9.9 * 10-19 J – 6.3 * 10-19 J = 3.6 * 10-19 J.

Answer: electrons escaping from the zinc surface can have a maximum kinetic energy Ek = 3.6 * 10-19 J.