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  4. Electrons having kinetic energy 30 eV are made to collide with atomic hydrogen gas (in ground state) and 42.5 % of electron energy is used to excite the hydrogen atoms. The number of emitted wavelengths in emission spectra are

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Q. Electrons having kinetic energy $30 \, eV$ are made to collide with atomic hydrogen gas (in ground state) and $42.5\%$ of electron energy is used to excite the hydrogen atoms. The number of emitted wavelengths in emission spectra are

NTA AbhyasNTA Abhyas 2020Atoms

Solution:

$42.5\%$ of $30 \, eV=12.75 \, eV$
$\therefore E_{4}-E_{1}=-0.85-\left(- 13.6\right)=12.75 \, eV$
So, it means electron has been transmitted from ground state to $3^{r d}$ excited state $\left(n = 4\right)$ , so total number of unique wavelengths emitted are
$=\frac{4 \times \left(4 - 1\right)}{2}=6$