AP EAPCET 05-Jul-2022 Shift 1 Paper

We know that, the radius (R) of nucleus is given as
R=R0A1∕3 or R∝A1∕3
Where,
R0‌=‌ constant ‌
A‌=‌ mass number ‌
∴ Nuclear density, ρ=‌

‌ mass ‌

‌ volume ‌

=‌

mA

4 3 πR3

(here, m is mass of each nucleon)
⇒‌‌ρ‌=‌

mA

4 3 π(R0A1∕3)3

=‌

mA

4 3 πR03A

ρ‌=‌

3m

4πR03

Hence, it is clear from above formula, nuclear density is independent of mass number A.
The binding energy, E=∆mc2
i. e E∝∆m
Where, ∆m= mass defect
Energy is released when heavy nuclei undergo transmutation into light nuclei.