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

According to Bohr.s model, `r_(m)=((m^(2))/(Z))xxr_(0)`
where m = orbit number, `r_(0)=` Bohr radius
For `""_(100)Fm^(257), Z=100 therefore m=5`
`therefore" "r_(m)=((5)^(2))/(100)r_(0)`
According to given problem
`nr_(0)=((5)^(2))/(100)r_(0) or n=(1)/(4)`