# What is the wavelength of a photon incident on the silver surface if the maximum

What is the wavelength of a photon incident on the silver surface if the maximum speed of photoelectrons is 250 km / s? the work function for silver is 4.7 eV.

V = 250 km / s = 250,000 m / s.

m = 9.1 * 10 ^ -31 kg.

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

c = 3 * 10 ^ 8 m / s.

Av = 4.7 eV = 7.52 * 10 ^ -19 J.

λ -?

Let us write down the condition of the photoelectric effect: h * c / λ = Av + Ek, where h * c / λ is the energy of the incident photons, Ek is the kinetic energy of electrons that fly out of the metal surface.

The kinetic energy of electrons Ek is determined by the formula: Ek = m * V ^ 2/2, where m is the mass of an electron, V is the velocity of the emitted electrons.

h * c / λ = Ab + m * V ^ 2/2.

λ = h * c / (Ab + m * V ^ 2/2).

λ = 6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s / (7.52 * 10 ^ -19 J + 9.1 * 10 ^ -31 kg * (250,000 m / s) ^ 2/2) = 0.25 * 10 ^ -6 m.

Answer: the incident light has a wavelength λ = 0.25 * 10 ^ -6 m. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.