A) \[\therefore \]
B) \[\frac{1}{\lambda }=109678\times {{(1)}^{2}}\left[ \frac{1}{{{(1)}^{2}}}-\frac{1}{{{(2)}^{2}}} \right]c{{m}^{-1}}\]
C) \[=\frac{109678\times 3}{4}c{{m}^{-1}}\]
D) \[\lambda =\frac{4\times {{10}^{7}}\times {{10}^{-7}}}{3\times 109678}cm\]
Correct Answer: C
Solution :
\[\because \] \[{{t}_{1/2}}=\frac{0.693}{1.35\times {{10}^{-13}}}s\] \[=5.13\times {{10}^{12}}s\] \[=1.628\times {{10}^{5}}yr.\] \[a-2r=\text{ }53pm\] \[4r=\sqrt{3}a\] \[2r=\frac{\sqrt{3}}{2}a\] \[\Rightarrow \] \[a-\frac{\sqrt{3}}{2}a=53\]
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