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

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsBohr’s Model and Physics of Atom5 Marks
Question
A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen $= 1.67 \times 10^{-27}kg.$
✓

Answer

Energy of the neutron is $\frac{1}{2}\text{mv}^2$
The condition for inelastic collision is,
$\frac{1}{2}\text{mv}^2>2\Delta\text{E}$
$\Delta\text{E}=\frac{1}{2}\text{mv}^2$
$\Delta\text{E}$ is the energy absorbed.
Energy required for first excited state is 10.2ev.
$\therefore\ \Delta\text{E}<10.2\text{ev}$
$\therefore10.2\text{ev}<\frac{1}{2}\text{mv}^2$
$\text{V}_\text{min}=\sqrt{\frac{4\times10.2}{\text{m}}}\text{ev}$
$\therefore\text{v}=\sqrt{\frac{10.2\times1.6\times10^{-19}\times4}{1.67\times10^{-27}}}=6\times10^4\text{m/sec}$

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