A 12/5 eV electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy. Level the hydrogen atoms would be excited ? Calculate the wavelengths of the first memeber of Lyman and first member of Balmer series.

Explanation

To solve the problem step by step, we will first determine the maximum energy level to which the hydrogen atoms can be excited by the 12.5 eV electron beam. Then, we will calculate the wavelengths of the first member of the Lyman and Balmer series.

### Step 1: Determine the Energy Levels of Hydrogen
The energy of the nth level of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number.
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