Question
Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3nm may be emitted by the hydrogen?

Answer

The given wavelength in Balmer series.
The first line, which requires minimum energy is from $n_1 = 3$ to $n_2= 2$
$\therefore$ The energy should be equal to the energy required for transition from ground state to $n = 3$
i.e., $\text{E}=13.6\Big[1-\Big(\frac{1}{9}\Big)\Big]=12.09\text{eV}$
$\therefore$ Minimum value of electric field $= 12.09v/m = 12.1v/m$

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