If the atom`(_100)Fm^(257)` follows the Bohr model the radius of `_(100)Fm^(257)` is `n` time the Bohr radius , then find `n` .

Options

A. `100`
B. `200`
C. `4`
D. `(1)/(4)`

Answer

D

Explanation

`(r_(m)) = ((m^(2))/(Z))(0.53 Å)`
`= (nxx0.53Å) rArr (m^(2))/(Z)= n`
`m = 5` for `_(100)Fm^(257)` (the outermost shell)
and `z = 100 rArrn = ((5)^(2))/(100) = (1)/(4)`