A) \[400\overset{\text{o}}{\mathop{\text{A}}}\,\]
B) \[300\overset{\text{o}}{\mathop{\text{A}}}\,\]
C) \[500\overset{\text{o}}{\mathop{\text{A}}}\,\]
D) \[600\overset{\text{o}}{\mathop{\text{A}}}\,\]
Correct Answer: B
Solution :
[b] The energy in the ground state \[{{E}_{1}}=-\,4Rydberg\text{ }{{E}_{1}}=-\,4\times 2.2\times {{10}^{-18}}J\] The energy of the first excited state (n=2) \[{{E}_{2}}=\frac{{{E}_{1}}}{4}=2.2\times {{10}^{-18}}J\] The energy difference \[\Delta E={{E}_{2}}-{{E}_{1}}=3\times 2.2\times {{10}^{-18}}J\] Now, the wavelength of radiation emitted is \[\lambda =\frac{hc}{\Delta E}\] \[\lambda =\frac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}{3\times 2.2\times {{10}^{-18}}}=300\overset{\text{o}}{\mathop{\text{A}}}\,\]
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