A) \[4125\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[3000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[6000\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[2062.5\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: B
Solution :
The maximum wavelength above which no photoelectron can emit from metal surface is called cut-off wavelength and is given by work function \[=\frac{hc}{\text{cut-off wavelength}}\] or cut-off wavelength \[=\frac{hc}{\text{work function}}\] \[\therefore \] \[{{\lambda }_{0}}=\frac{hc}{W}\] ...(i) Given, \[h=6.6\times {{10}^{-34}}\,J-s\] \[c=3\times {{10}^{8}}\,m/s\] \[W=4.125\,eV=4.125\times 1.6\times {{10}^{-19}}\,J\] Substituting the given values in Eq. (i), we get \[{{\lambda }_{0}}=\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}{4.125\times 1.6\times {{10}^{-19}}}\overset{\text{o}}{\mathop{\text{A}}}\,\] \[=3\times {{10}^{-7}}\,m=3000\,\,\overset{\text{o}}{\mathop{\text{A}}}\,\]
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