If the number of alpha particles scattered at | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The number of scattered particles $N$ is related to the scattering angle $	heta$ by the Rutherford scattering formula: $N \propto \frac{1}{\sin^4

Vedclass · Accepted Answer

$224$

Vedclass · Answer

(A) The number of scattered particles $N$ is related to the scattering angle $	heta$ by the Rutherford scattering formula: $N \propto \frac{1}{\sin^4(	heta/2)}$.Given $N_1 = 56$ at $	heta_1 = 90^\circ$,we need to find $N_2$ at $	heta_2 = 60^\circ$.Using the ratio: $\frac{N_2}{N_1} = \left[ \frac{\sin(	heta_1/2)}{\sin(	heta_2/2)} ight]^4$.Substituting the values: $\frac{N_2}{56} = \left[ \frac{\sin(90^\circ/2)}{\sin(60^\circ/2)} ight]^4 = \left[ \frac{\sin(45^\circ)}{\sin(30^\circ)} ight]^4$.Since $\sin(45^\circ) = \frac{1}{\sqrt{2}}$ and $\sin(30^\circ) = \frac{1}{2}$,we have $\frac{\sin(45^\circ)}{\sin(30^\circ)} = \frac{1/\sqrt{2}}{1/2} = \frac{2}{\sqrt{2}} = \sqrt{2}$.Therefore,$\frac{N_2}{56} = (\sqrt{2})^4 = 4$.$N_2 = 56 	imes 4 = 224$.

If the number of alpha particles scattered at an angle of $90^\circ$ is $56$,how many particles will be scattered at an angle of $60^\circ$?

Similar Questions

What is the plum pudding model of the atom?

Using Thomson's model of the atom,consider an atom consisting of two electrons,each of charge $-e$,embedded in a sphere of charge $+2e$ and radius $R$. In equilibrium,each electron is at a distance $d$ from the center of the atom. What is the equilibrium separation between the electrons?

The diagram shows the path of four $\alpha$-particles of the same energy being scattered by the nucleus of an atom. Which of these is/are not physically possible?

In the Rutherford experiment,$\alpha$-particles are scattered as shown in the figure. Which of the four paths is not possible?

In the Rutherford experiment,for a head-on collision of $\alpha$-particles with a gold nucleus,the impact parameter is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module