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What is the minimum energy that must be given to a \mathrm{H} atom in ground state so that it can emit an \mathrm{H}_\gamma line in Balmer series?

Option: 1

13.06 eV


Option: 2

12.75 eV


Option: 3

10.2 eV


Option: 4

2.86 eV


Answers (1)

best_answer

\mathrm{H}_\gamma line in the Balmer series corresponds to transition from \mathrm{n}=5 \: \text{to}\: \mathrm{n}=2
Therefore, electron in the ground state \mathrm{(n=1)} must be raised first to the state \mathrm{(n=5)}.

The minimum energy required for this purpose is

\begin{aligned} & \mathrm{E}=\mathrm{E}_5-\mathrm{E}_1 \\ \\& =-\frac{13.6}{5^2} \mathrm{eV}-\left(-\frac{13.6}{1^2} \mathrm{eV}\right) \quad\left(\text { As } \mathrm{E}_{\mathrm{n}}=-\frac{13.6}{\mathrm{n}^2} \mathrm{eV}\right) \\ \\& =-0.54 \mathrm{eV}+13.6 \mathrm{eV}=13.06 \mathrm{eV} \end{aligned}

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SANGALDEEP SINGH

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