A) 900
B) 2025
C) 32400
D) 4050
Correct Answer: A
Solution :
Number of \[\alpha -\]particles scattered through angle \[\theta \] \[N\propto \frac{1}{{{\sin }^{4}}\left( \frac{\theta }{2} \right)}\] or \[\frac{{{N}_{1}}}{{{N}_{2}}}=\frac{\left( {{\sin }^{4}}\frac{{{\theta }_{2}}}{2} \right)}{\left( {{\sin }^{4}}\frac{{{\theta }_{1}}}{2} \right)}\] or \[\frac{8100}{{{N}_{2}}}=\frac{\left( {{\sin }^{4}}\frac{120}{2} \right)}{\left( {{\sin }^{4}}\frac{60}{2} \right)}\] or \[\frac{8100}{{{N}_{2}}}=\frac{{{\sin }^{4}}60}{{{\sin }^{4}}30}\] \[\Rightarrow \] \[{{N}_{2}}=\frac{8100\times \frac{1}{16}}{\frac{9}{16}}\] or \[{{N}_{2}}=900\]
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