The work function of an electron from cadmium is 4.08 eV, which is the wavelength of light.

The work function of an electron from cadmium is 4.08 eV, which is the wavelength of light. falling on the surface of cadmium, if the maximum speed of photoelectrons is 7.2 x 10 ^ 5 m / s.

According to Einstein’s equation h ∙ ν = Av + ​​(m ∙ v ^ 2) / 2, the photon energy h ∙ ν during the photoelectric effect is spent on performing the work function of the electron from the atom Av and giving it kinetic energy (m ∙ v ^ 2) / 2, where h = 6.62 ∙ 10 ^ (- 34) J ∙ s is Planck’s constant, ν is the frequency of light emission, m = 9.1 ∙ 10 ^ (- 31) is the mass of an electron, v is its velocity. It is known that the work function of an electron from cadmium Av = 4.08 eV = 4.08 ∙ 1.6 ∙ 10 ^ (- 19) J. To determine what is the wavelength of light falling on the surface of cadmium, it is necessary to express the frequency of light through its wavelength λ and speed of light c = 3 ∙ 10 ^ 8 m / s. We get: ν = с / λ. Since the maximum speed of photoelectrons is v = 7.2 ∙ 10 ^ 5 m / s, then h ∙ s / λ = Av + ​​(m ∙ v ^ 2) / 2 or λ = h ∙ s / (Av + (m ∙ v ^ 2) / 2). Substituting the values, we get λ = 6.62 ∙ 10 ^ (- 34) ∙ 3 ∙ 10 ^ 8 / (4.08 ∙ 1.6 ∙ 10 ^ (- 19) + (9.1 ∙ 10 ^ (- 31) ∙ (3 ∙ 10 ^ 8) ^ 2): 2) ≈ 2.23 ∙ 10 ^ (- 7) (m).
Answer: 2.23 ∙ 10 ^ (- 7) m.