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 $656.3\ nm$ 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 $n_1 = 3$ 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 $= 12.09\ v/m = 12.1\ v/m$

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