Question

Assertion : Density of all the nuclei is same. 

Reason : Radius of nucleus is directly proportional to the cube root of mass number.

(a) Both A and R are true and R is the correct explanation of A

(b) Both A and R are true but R is not correct explanation of A

(c) A is true but R is false

(d) A and R are false

Answer 1

The correct option is (a) Both A and R are true and R is the correct explanation of A.

Explanation:

Experimentally, it is found that the average radius of a nuleus is given by

R = R_oA^1/3 where R_o = 1.1 x 10^-15 m = 1.1 fm and A = mass number

The volume of a nucleus is v

Now as the masses of a proton and a neutron are roughly equal, say m, the mass of a nucleus is also roughly proportional to the mass number A, M = mA. Hence density within a nucleus,

is independent of the mass number A.