A) \[R=-\left( \frac{1}{4\pi {{\varepsilon }_{0}}} \right).\frac{2{{\pi }^{2}}m{{e}^{2}}}{c{{h}^{2}}}\]
B) \[R=\left( \frac{1}{4\pi {{\varepsilon }_{0}}} \right).\frac{2{{\pi }^{2}}m{{e}^{4}}}{c{{h}^{2}}}\]
C) \[R={{\left( \frac{1}{4\pi {{\varepsilon }_{0}}} \right)}^{2}}.\frac{2{{\pi }^{2}}m{{e}^{4}}}{{{c}^{2}}{{h}^{2}}}\]
D) \[R={{\left( \frac{1}{4\pi {{\varepsilon }_{0}}} \right)}^{2}}.\frac{2{{\pi }^{2}}m{{e}^{4}}}{c{{h}^{3}}}\]
Correct Answer: D
Solution :
\[R=\frac{2{{\pi }^{2}}{{k}^{2}}{{e}^{4}}m}{c{{h}^{3}}}={{\left( \frac{1}{4\pi {{\varepsilon }_{0}}} \right)}^{2}}\frac{2{{\pi }^{2}}m{{e}^{4}}}{c{{h}^{3}}}\]
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