The sodium plate is irradiated with light, the wavelength of which is 66 nm. Determine the speed

The sodium plate is irradiated with light, the wavelength of which is 66 nm. Determine the speed of the photoelectrons if the work function is 4 * 10 ^ -19 J

Data: λ (light wavelength) = 66 nm (66 * 10 ^ -9) m; A (work function of electrons) = 4 * 10 ^ -19 J.

Constants: C (speed of a light wave) = 3 * 10 ^ 8 m / s; h (Planck’s constant) = 6.626 * 10 ^ -34 J * s, m (electron mass) = 9.1 * 10 ^ -31 kg.

The speed of photoelectrons is determined from the formula: h * ν = h * C / λ = A + Eк = A + 0.5 * m * V ^ 2, whence 0.5 * m * V ^ 2 = h * C / λ – A and V = √ ((h * C / λ – A) / 0.5 * m).

V = √ ((6.626 * 10 ^ -34 * 3 * 10 ^ 8 / (66 * 10 ^ -9) – 4 * 10 ^ -19) / 0.5 * 9.1 * 10 ^ -31) ≈ 2 , 4 * 10 ^ 6 m / s.