Order of magnitude of density of uranium nucleus is

Options

A. `10^20 kg//m^3`
B. `10^17 kg//m^3`
C. `10^14 kg//m^3`
D. `10^11 kg//m^3`

Answer

B

Explanation

(b) The order of magnitude of mass and volume of uranium nucleus will be
`m square (1.67 xx 10^-27 kg)` (`A` is atomic number)
`V = (4)/(3) pi r^3 ~= (4)/(3)[(1.25 xx 10^-15 m)A^(1//3)]^3`
`~=(8.2 xx 10^-45 m^3) A`
Hence, `rho = (m)/(V) = (A(1.67 xx 10^-27 kg))/((8.2 xx 10^-45 m^3)A)`
`~= 2.0 xx 10^17 kg//m^3`.