Question

White light, with frequencies ranging from 4.00 x 10^14 Hz to 7.90 x 10^14 Hz, is incident on a barium surface. Given that the work function of barium is 2.52 eV, find:
(a) the maximum kinetic energy of electrons ejected from this surface.
(b) the range of frequencies for which no electrons are ejected.

Answer 1

Answer:

0.7515875 eV

$4\times 10^{14}\leq f$

Explanation:

f = Maximum frequency = $7.9\times 10^{14}\ Hz$

h = Planck's constant = $6.626\times 10^{-34}\ m^2kg/s$

W = Work function = 2.52 eV

Converting to Joules

$W=2.52\times 1.6\times 10^{-19}\\\Rightarrow W=4.032\times 10^{-19}\ J$

Maximum photon energy is given by

$E=hf\\\Rightarrow E=6.626\times 10^{-34}\times 7.9\times 10^{14}\\\Rightarrow E=5.23454\times 10^{-19}\ J$

Maximum Kinetic energy is given by

$K=E-W\\\Rightarrow K=5.23454\times 10^{-19}-4.032\times 10^{-19}\\\Rightarrow K=1.20254\times 10^{-19}\ J$

Converting to eV

$1.20254\times 10^{-19}\times \frac{1}{1.6\times 10^{-19}}=0.7515875\ eV$

The maximum kinetic energy of electrons ejected from this surface is 0.7515875 eV

$W=hf\\\Rightarrow f=\frac{W}{h}\\\Rightarrow f=\frac{4.032\times 10^{-19}}{6.626\times 10^{-34}}\\\Rightarrow f=6.08512\times 10^{14}\ Hz$

The range of frequencies for which no electrons are ejected is

$4\times 10^{14}\leq f$