A 12.5 eV electron beam is used to bombard g | vedclass

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(A) The energy levels of a hydrogen atom are given by $E_n = -\frac{13.6}{n^2} \ eV$.At room temperature,hydrogen atoms are in the ground state $(n=1)

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$2$ lines in the Lyman series and $1$ line in the Balmer series

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(A) The energy levels of a hydrogen atom are given by $E_n = -\frac{13.6}{n^2} \ eV$.At room temperature,hydrogen atoms are in the ground state $(n=1)$.The energy required to excite an electron from $n=1$ to $n=2$ is $E_2 - E_1 = -3.4 - (-13.6) = 10.2 \ eV$.The energy required to excite an electron from $n=1$ to $n=3$ is $E_3 - E_1 = -1.51 - (-13.6) = 12.09 \ eV$.The energy required to excite an electron from $n=1$ to $n=4$ is $E_4 - E_1 = -0.85 - (-13.6) = 12.75 \ eV$.Since the incident electron beam has an energy of $12.5 \ eV$,it can excite hydrogen atoms up to the $n=3$ energy level.When these excited atoms return to the ground state,the possible transitions are:$n=3 \rightarrow n=2$ (Balmer series)$n=3 \rightarrow n=1$ (Lyman series)$n=2 \rightarrow n=1$ (Lyman series)Thus,there are $2$ lines in the Lyman series and $1$ line in the Balmer series.

$A$ $12.5 \ eV$ electron beam is used to bombard gaseous hydrogen at room temperature. It will emit:

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