Answer to Question #222840 in Quantum Mechanics for Akshat

Question

The work function of sodium metal is 2.3 eV. What is the longest wavelength of light that cause
photoelectric emission from sodium

Answer 1

The longest wavelength corresponds to the smallest energy of photon. When the electron catches the photon, the energy of the photon transforms into the sum of the work function and the kinetic energy of the electron released. The minimum energy of photon should be enough to ionize the atom, so the smallest needed energy of photon is equal to the work function.

$E =h\nu =hc/\lambda = A, \; \lambda = hc/A.$

1 eV = $1.6\cdot10^{-19}$ J,

$\lambda = \dfrac{hc}{A}, \\ \lambda =\dfrac{6.63\cdot10^{-34}\,\mathrm{J \cdot s}\cdot 3\cdot 10^8\,\mathrm{m/s}} {2.3\cdot1.6\cdot10^{-19}}= 5.4\cdot10^{-7}\,\mathrm{m}.$