Electrons are emitted from an electron gun at almost zero velocit… - Vidyadip

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?

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Answer

The given wavelength in Balmer series.
The first line, which requires minimum energy is from n₁ = 3 to n₂= 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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