Question

Rutherford's experiments suggested that the size of the nucleus is about

• A. ${10}^{-14}m$ to ${10}^{-15}m$
• B. ${10}^{-15}m$ to ${10}^{13}m$
• C. ${10}^{-15}m$ to ${10}^{14}m$
• D. ${10}^{-15}m$ to ${10}^{16}m$

Answer 1

Answer: (A)

${10}^{-14}m$ to ${10}^{-15}m$

To estimate the size of the nucleus Rutherford performed an experiment of Scattering of Alpha particle from the nucleus which is considered as a Point charge particle.

The potential of the particle that touches the nucleus is given as $10.4MeV$

He assumed that all the K.E. lost should be equal to all the P.E. that is being gained

$K.E.lost=P.E.gained$

$r=\frac{2\times 97e\cdot 4\pi {\epsilon }_0}{10.4MeV}$

$r=\frac{2\times 97\times 1.6\times {10}^{19}\times 8.9\times {10}^9}{10.4\times {10}^6}$

By solving the above equation we get

$r=3.6\times {10}^{-15}m$

If the electron is stopped and turned back then the potential energy will be $7.7MeV$

By substituting the potential in the above equation we get

$r=\frac{2\times 97\times 1.6\times {10}^{19}\times 8.9\times {10}^9}{7.7\times {10}^6}$

$r=3.6\times {10}^{-14}m$