Question

If the work function of a material is such that red light of wavelength 700 nm just barely initiates the photoelectric effect, what must the maximum kinetic energy of ejected electrons be when violet light of wavelength 400 nm illuminates the material? Express your answer with the appropriate units.

Answer 1

Answer:

2.13 x 10^-19 J or 0.53 eV

Explanation:

cut off wavelength, λo = 700 nm = 700 x 10^-9 m

λ = 400 nm = 400 x 10^-9 m

Use the energy equation

$E = \frac{h c}{\lambda _{o}}+K$

Where, K be the work function

$\frac{h c}{\lambda} = \frac{h c}{\lambda _{o}}+K$

$K =hc\left ( \frac{1}{\lambda } -\frac{1}{\lambda _{0}}\right )$

$K =6.63\times 10^{-34}\times 3\times 10^{8}\left ( \frac{1}{4\times 10^{-7} } -\frac{1}{7\times 10^{-7}}\right )$

K = 2.13 x 10^-19 J

K = 0.53 eV