A) 20
B) 29
C) 40
D) 59
Correct Answer: C
Solution :
The wavelength of X-ray lines is given by \[\frac{1}{\lambda }=R{{Z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\] where R is Rydbergs constant. The \[{{K}_{\alpha }}\] line characteristic of an element is produced due to transition from the L shell \[({{n}_{2}}=2)\] to the K shell \[({{n}_{1}}=1)\].Thus, \[\frac{1}{\lambda }=R{{Z}^{2}}\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)\] \[=\frac{3}{4}R{{Z}^{2}}\] or \[{{Z}^{2}}=\frac{4}{3R\lambda }\] \[=\frac{4}{3\,(1.097\times {{10}^{7}}\times (0.76)\times {{10}^{-10}})}\] = 1599.25 or \[{{Z}^{2}}\approx 1600\] or Z = 40.
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