In the study of Geiger-Marsdon experiment on scattering of $straight alpha$ particles by a thin foil of gold, draw the trajectory of -particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study. From the relation $straight R space equals space straight R subscript straight o space straight A to the power of begin inline style bevelled 1 third end style end exponent$ where R_o is constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A.

Solution

Consider an alpha-particle with initial K.E = $1 half m space v squared$ directed towards the center of nucleus of an atom.
The force that exists between nucleus and α-particle is Coulomb’s repulsive force. On account of this force, at the distance of closest approach $r subscript o$ , the particle stops and cannot go further closer to the nucleus. And, K.E gets converted to P.E.
That is,
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Hence, we can see that the size of the nucleus is approximately equal to the distance of closest approach, r_o .

Now,

If ‘m’ is the average mass of the nucleon and r the radius of nucleus, then

Mass of nucleus = mA; where A is the mass number of the element.
Volume of the nucleus, $straight V space equals space 4 divided by 3 space πR cubed$
This implies,
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Therefore, the nuclear density is independent of mass number A.

Some More Questions From Wave Optics Chapter

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson's model much less, about the same, or much greater than that predicted by Rutherford's model?

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

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