Answer
(a) The metals which will exhibit the photoelectric effect are potassium and sodium.
(b) The metals which will exhibit the photoelectric effect are potassium, sodium, aluminum, tungsten, copper, and iron.
Work Step by Step
(a) We can find the energy of a photon with a wavelength $\lambda = 400~nm$:
$E = \frac{hc}{\lambda}$
$E = \frac{(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{400\times 10^{-9}~m}$
$E = 4.9695\times 10^{-19}~J$
$E = (4.9695\times 10^{-19}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 3.11~eV$
The metals which will exhibit the photoelectric effect are those metals with a work function that is less than $3.11~eV$
The metals which will exhibit the photoelectric effect are potassium and sodium.
(b) We can find the energy of a photon with a wavelength $\lambda = 250~nm$:
$E = \frac{hc}{\lambda}$
$E = \frac{(6.626\times 10^{-34}~J~s)(3.0\times 10^8~m/s)}{250\times 10^{-9}~m}$
$E = 7.9512\times 10^{-19}~J$
$E = (7.9512\times 10^{-19}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 4.97~eV$
The metals which will exhibit the photoelectric effect are those metals with a work function that is less than $4.97~eV$
The metals which will exhibit the photoelectric effect are potassium, sodium, aluminum, tungsten, copper, and iron.
