If, the binding energy of electrons in a metal is \(250 \mathrm{~kJ} / \mathrm{mol}\), what should be the…
If, the binding energy of electrons in a metal is \(250 \mathrm{~kJ} / \mathrm{mol}\), what should be the threshold frequency of the striking photons in order to free an electron from the metal surface?
\(6.26 \times 10^{14} \mathrm{~s}^{-1}\)
\(12.4 \times 10^{14} \mathrm{~s}^{-1}\)
\(6.26 \times 10^{12} \mathrm{~s}^{-1}\)
\(12.4 \times 10^{12} \mathrm{~s}^{-1}\)
Solution
Binding energy of 1 mole of electrons \(=250 \mathrm{~kJ}\) Binding energy of 1 electron
\(\begin{aligned}
& =(250) /\left(6.022 \times 10^{23}\right) \mathrm{kJ} \\
& =4.15 \times 10^{-22} \mathrm{~kJ} \\
& =4.15 \times 10^{-19} \mathrm{~J}
\end{aligned}\)
Threshold energy \(\left(h v_0\right)=\) Binding energy
\(\begin{aligned}
\therefore h v_0 & =4.15 \times 10^{-19} \mathrm{~J} \\
\text {or } v_0 & =\left(4.15 \times 10^{-19} \mathrm{~J}\right) / h \\
& =\left(4.15 \times 10^{19} \mathrm{~J}\right)\left(6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s}\right) \\
& =6.26 \times 10^{14} \mathrm{~s}^{-1}
\end{aligned}\)
Hence, the correct option is (a).