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Bohr’s Model and Physics of Atom — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsBohr’s Model and Physics of Atom2 Marks
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?
✓

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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