Question 16

A hydrogen atom in ground state is given an energy of $$10.2 \text{ eV}$$. How many spectral lines will be emitted due to transition of electrons?

Ground state energy of hydrogen: $$E_1 = -13.6$$ eV. Energy given = 10.2 eV.

Total energy = $$-13.6 + 10.2 = -3.4$$ eV = $$-\frac{13.6}{n^2}$$. So $$n^2 = 4$$, $$n = 2$$.

The electron goes to $$n = 2$$. Spectral lines from transitions: $$n=2 \to n=1$$.

Number of spectral lines = $$\frac{n(n-1)}{2} = \frac{2 \times 1}{2} = 1$$.

The correct answer is Option 4: 1.

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