Question

Light of frequency $8.41\times {10}^{14}Hz$ is incident on a metal surface. Electrons with a maximum speed of $7.5\times {10}^5$ ${ms}^{-1}$ are ejected from the surface. Calculate the threshold frequency for photo emission of electrons. Also find the work function of the metal in electron volt (eV). Given, Planck's constant $h=6.625\times {10}^{-34}J{s}^{-1}$ and mass of the electron $9.1\times {10}^{-31}Kg$.

Answer 1

$v=8.41\times {10}^{14}Hz$

$V_{max}=7.5\times {10}^{5}m{s}^{-1}$

$h=6.625\times {10}^{-34}J{s}^{-1}$

$m=9.1\times {10}^{-31}kg$
$hv={\varphi }_0+K_{max}$
$hv=h{v}_0+\frac{1}{2}m{V}_{max}^2$
$hv-h{v}_0=\frac{1}{2}m{V}_{max}^2$
$(v-v_0)=\frac{1}{2h}m{V}_{max}^2=\frac{1}{2\times 6.625\times {10}^{-34}}\times 9.1\times {10}^{-31}\times {(7.5\times {10}^5)}^2$
$(v-v_0)=3.8632\times {10}^{14}$

$v_0=8.41\times {10}^{14}-3.8632\times {10}^{14}=4.5468\times {10}^{14}Hz$

${\varphi }_0=h{v}_0=6.625\times {10}^{-34}\times 4.5468\times {10}^{14}=3.01226\times {10}^{-19}$

${\varphi }_0=\frac{3.01226\times {10}^{-19}}{1.6\times {10}^{-19}}=1.8826eV$