In a Geiger-Marsden α -particle scattering experiment, the number of α -particles scattered at an angle of 60^ is N per minute. What will be the number of α -particles scattered at an angle of 120^ in the same time

Question

Quantrex Academy · Accepted Answer

Correct answer: A. (N)/(9)

According to Rutherford's scattering formula, the number of

\alpha

-particles scattered at an angle

\theta

is given by:

N(\theta) \propto \dfrac{1}{\sin^4(\theta/2)}

Taking the ratio of the number of particles scattered at

120^\circ

and

60^\circ

:

\dfrac{N(120^\circ)}{N(60^\circ)} = \dfrac{\sin^4(60^\circ/2)}{\sin^4(120^\circ/2)}

\dfrac{N(120^\circ)}{N} = \dfrac{\sin^4(30^\circ)}{\sin^4(60^\circ)}

\dfrac{N(120^\circ)}{N} = \dfrac{(1/2)^4}{(\sqrt{3}/2)^4} = \dfrac{1/16}{9/16} = \dfrac{1}{9}

Therefore,

N(120^\circ) = \dfrac{N}{9}

.

Answer:

\dfrac{N}{9}

In a Geiger-Marsden α -particle scattering experiment, the number...

Options

Correct answer

Step-by-step solution

More from Atomic Physics