JEE Mains · Physics · STD 12 - 12. atoms
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength \(980\,\mathop A\limits^o \). The radius of the atom in the excited state, in terms of Bohr radius \(a_0,\) will be \((hc\,=\,12500\,eV-\mathop A\limits^o)\)
- A \(25\,a_0\)
- B \(9\,a_0\)
- C \(16\,a_0\)
- D \(4\,a_0\)
Answer & Solution
Correct Answer
(C) \(16\,a_0\)
Step-by-step Solution
Detailed explanation
Energy supplied \(E=\frac{12400}{900}=12.65 \mathrm{eV}\) \(\therefore \mathrm{E}_{\mathrm{n}}-\mathrm{E}_{1}=12.65\) \(\Rightarrow(13.6)\left(1-\frac{1}{n^{2}}\right)=12.65\) \(\Rightarrow n^{2} \approx 14.3\) \(\Rightarrow n \approx 4\) \(r \propto n^{2}\)
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