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Atoms & Nuclei

JEE Main level, numerical answer, medium

113 of 239

Question 113 of 239

Hydrogen atom is bombarded with electrons accelerated through a potential different of $V$ , which causes excitation of hydrogen atoms. If the experiment is being formed at $T=0K$ . The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $\dfrac{\alpha }{10}V$ , where $\alpha =$ _________.(Write the value to the nearest integer)

Show answer and solution

Answer: 121

For minimum potential difference, electron has to make transition from

n=3

n=2

state but first electron has to reach to

n=3

state from ground state. So, energy of bombarding electron should be equal to energy difference of

n=3

and

n=1

state.

\Delta E=13.6\left[1-\dfrac{1}{{3}^{2}}\right]e=eV

\Rightarrow \dfrac{13.6\times 8}{9}=V

\Rightarrow V=12.09V\approx 12.1V

So,

\alpha =121

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