In a Rutherford's α-scattering experiment with thin gold foil, 8100 scintillations per minute are observed at an angle of 60°. What will be the number of scintillations per minute at an angle of 120°?

Solution

Given,
Number of scintillations per minute at an angle 60°, n₁ = 8100 m
Number of scintillations per minute at an angle 120° , n₂ =?

The scattering in the Rutherford's experiment is proportional to cot^{4 $\frac{ϕ}{2} .$}

\Rightarrow

\frac{n_{2}}{n_{1}} = \frac{\cot^{4} ϕ_{2} / 2}{\cot^{4} ϕ_{1} / 2}

Therefore,

^{$\frac{n_{2}}{n_{1}} = \frac{\cot^{4} (\frac{120 °}{2})}{\cot^{4} (\frac{60 °}{2})} = \frac{\cot^{4} 60 °}{\cot^{4} 30 °} = {(\frac{\frac{1}{\sqrt{3}}}{\sqrt{3}})}^{4} = \frac{1}{81}$
This implies,

$n_{2} = \frac{1}{81} \times n_{1} = \frac{1}{81} \times 8100 = 100 .$}

Some More Questions From Wave Optics Chapter

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

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Wave Optics

In a Rutherford's α-scattering experiment with thin gold foil, 8100 scintillations per minute are observed at an angle of 60°. What will be the number of scintillations per minute at an angle of 120°?

Some More Questions From Wave Optics Chapter

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

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For Daily Free Study Material Join wiredfaculty

Wave Optics

In a Rutherford's α-scattering experiment with thin gold foil, 8100 scintillations per minute are observed at an angle of 60°. What will be the number of scintillations per minute at an angle of 120°?

Some More Questions From Wave Optics Chapter

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a _____________ but has a highly non-uniform mass distribution in __________ (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)