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When electromagnetic radiation of wavelength 300 nm falls on the surface of a metal, electrons are emitted with the kinetic energy of $1.68\times10^5$ J mol$^{-1}$. What is the minimum energy needed to remove an electron from the metal? ($h=6.626\times10^{-34}$ Js, $c=3\times10^8$ ms$^{-1}$, $N_A=6.022\times10^{23}$ mol$^{-1}$)
Detailed Solution
$E_p=\frac{hc}{\lambda}N_A=\frac{6.626\times10^{-34}\times3\times10^8}{300\times10^{-9}}\times6.022\times10^{23}=3.99\times10^5$ J mol$^{-1}$. $\phi=E_p-KE=(3.99-1.68)\times10^5\approx2.31\times10^5$ J mol$^{-1}$.