CBSE Class 12 · 2015 · Delhi · Modern PhysicsShort Answer

In the study of the Geiger-Marsden experiment on scattering of

α

-particles by a thin foil of gold, draw the trajectory of

α

-particles in the Coulomb field of the target nucleus. Explain briefly how one gets information on the size of the nucleus from this study. From the relation

R = R_{0} A^{1/3}

, where

R_{0}

is a constant and

A

is the mass number of the nucleus, show that nuclear matter density is independent of

A

Answer: Closest-approach distance gives nuclear size; $ρ = 3 m /4 π R_{0}^{3}$ independent of $A$ .

Solution

The

α

-particles follow hyperbolic paths in the Coulomb field of the nucleus; those aimed nearly head-on are deflected through large angles, even close to

18 0^{\circ}

(see trajectory diagram).
For a head-on collision the

α

-particle momentarily stops at the distance of closest approach, where all its kinetic energy has become electrostatic potential energy. This distance gives an upper limit to the size of the nucleus.
For nuclear density, with

R = R_{0} A^{1/3}

and mass

\approx A m

ρ = \frac{A m}{\frac{4}{3} π ( R _{0} A ^{1/3} ) ^{3}} = \frac{A m}{\frac{4}{3} π R _{0}^{3} A} = \frac{3 m}{4 π R _{0}^{3}},

which is independent of

A

ρ = \frac{3 m}{4 π R _{0}^{3}} (independent of A)

CBSE Class 12 Board · 2015 · Delhi · Subjective

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CBSE Class 12 · 2015 · Delhi · Modern PhysicsShort Answer

Solution

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