CBSE Class 12 · 2012 · Modern PhysicsShort Answer

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(i) What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number

A

lying

30 < A < 170

?
(ii) Show that the density of a nucleus over a wide range of nuclei is constant — independent of mass number

A

Answer: Saturation of nuclear force; $ρ = 3 m /4 π R_{0}^{3}$ independent of $A$ .

Solution

(i) The near-constant BE/A in this range is a consequence of the saturation (short-range) property of the nuclear force: each nucleon interacts only with its few nearest neighbours, so the binding per nucleon does not keep increasing as more nucleons are added.
(ii) With

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

and nuclear mass

\approx A m

ρ = \frac{mass}{volume} = \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 · 2012 · Subjective

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CBSE Class 12 · 2012 · Modern PhysicsShort Answer

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