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 = 0 K . The minimum potenti

Question

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 = 0 K . The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be 10 α ​ V , where α = _________.(Write the value to the nearest integer)

TestHub · Accepted Answer

For minimum potential difference, electron has to make transition from $n = 3$ to $n = 2$ 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.

$Δ E = 13.6 [1 - \frac{1}{3 ^{2}}] e = e V$

$\Rightarrow \frac{13.6 \times 8}{9} = V$

$\Rightarrow V = 12.09 V \approx 12.1 V$

So, $α = 121$ .

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