Atoms And Nuclei Question 286
Question: In a Rutherford experiment, the number of particles scattered at $ 90{}^\circ $ angle are 28 per minute then number of scattered particles at an angle $ ~60{}^\circ $ and $ 120{}^\circ $ will be
Options:
A) 117 per minute, 25 per minute
B) 50 per minute, 12.5 per minute
C) 100 per minute, 200 per minute
D) 112 per minute, 12.4 per minute
Show Answer
Answer:
Correct Answer: D
Solution:
- No. of particles scattered through an angle
$ \theta =N( \theta )=\frac{kZ^{2}}{{{\sin }^{4}}( \frac{\theta }{2} ){{( K.E. )}^{2}}} $
$ \therefore 28=\frac{4kcz^{2}}{{{( K.E. )}^{2}}}\text{ for }\theta \text{=90}{}^\circ $
$ \therefore \frac{kcz^{2}}{{{( K.E. )}^{2}}}\text{ =}\frac{28}{4}=7 $
$ \therefore N( 60{}^\circ )=\frac{7}{{{\sin }^{4}}( \frac{60{}^\circ }{2} )}=16\times 7=112/\min . $ $ N( 120{}^\circ )=\frac{7}{\sin ( \frac{120{}^\circ }{2} )}=12.4/\min $
