Nuclear Physics and RadioactivityHard

Question

$7.9MeV\alpha$-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) $\_\_\_\_$ m.

$\left\lbrack \frac{1}{4\pi\epsilon_{o}} = 9 \times 10^{9}{Nm}^{2}/C^{2} \right.\ $ and electron charge $\left. \ = 1.6 \times 10^{- 19}C \right\rbrack$

Options

A.$5.76 \times 10^{- 14}$
B.$1.44 \times 10^{- 13}$
C.$2.88 \times 10^{- 14}$
D.$1.69 \times 10^{- 12}$

Solution

By mechanical energy conservation

$${(Me)_{i} = (Me)_{f} }{{PE}_{i} + {KE}_{i} = {PE}_{f} + {KE}_{f} }{0 + 7.9 \times 10^{6} \times 1.6 \times 10^{- 19} = \frac{k(2e)(Ze)}{r} + 0 }{r = \frac{9 \times 10^{9} \times 2 \times \left( 1.6 \times 10^{- 19} \right)^{2} \times 79}{7.9 \times 10^{6} \times 1.6 \times 10^{- 19}} = 2.88 \times 10^{- 14}\text{ }m }$$For diameter ⇒ D = $2r = 5.76 \times 10^{- 14}\text{ }m$

Create a free account to view solution

View Solution Free
Topic: Nuclear Physics and Radioactivity·Practice all Nuclear Physics and Radioactivity questions

More Nuclear Physics and Radioactivity Questions

In a hydrogen atom, the electron is in nth exited state. It any com down to second exited state by emitting ten differen...Figure shows the graph of stopping potential versus the frequency of a photosensitive metal. The plank′s constant ...A radioactive sample disintegrates by 10% during one month. How much fraction will disintegrate in four months :-...An archaeologist analyses the wood in a prehistoric structure and finds that C14 (Half life = 5700 years) to C12 is only...Light of two different frequencies whose photons have energies of 1eV and 2.5 eV are incident one by one on a metal surf...