CBSE Class 12 · 2019 · Modern PhysicsShort Answer

(a) Explain briefly how Rutherford scattering of

α

-particles by a target nucleus can provide information on the size of the nucleus.
(b) Show that the density of a nucleus is independent of its mass number

A

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

Solution

(a) In a nearly head-on collision an

α

-particle is brought momentarily to rest at the distance of closest approach, where its whole kinetic energy has turned into electrostatic potential energy. This distance,

r_{0} = \frac{k Z e ^{2}}{K}

(where

K

is the

α

-particle's energy), sets an upper limit on the nuclear radius, giving information about the size of the nucleus.
(b) With

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

and nuclear mass

\approx A m

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

independent of

A

r_{0} = \frac{k Z e ^{2}}{K}; ρ = \frac{3 m}{4 π R _{0}^{3}}

CBSE Class 12 Board · 2019 · Subjective

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CBSE Class 12 · 2019 · Modern PhysicsShort Answer

Solution

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