The nuclear radius of a nucelus with nucleon number `16` is `3 xx 10^(-15) m`. Then, the nuclear radius of a nucleus with nucleon number `128` is .

Options

A. `3 xx 10^-15 m`
B. `1.5 xx 10^-15 m`
C. `6 xx 10^-15 m`
D. `4.5 xx 10^-15 m`

Answer

C

Explanation

( c) Radius `R` of nucleus changes with the nucleon number `A` of the nucleus as
`R = 1.3 xx 10^-15 xx A^(1//3) metre`
Hence `(R_2)/(R_1) ((A_2)/(A_1))^(1//3) = ((128)/(16))^(1//3) = (8)^(1//3) = 2`
`:. R_2 = 2 R_1 = 2 (3 xx 10^-15)_(metre)`
=`6 xx 10^-15 metre`.