Question

If the atom ${}_{100}^{257}Fm$ follows the Bohr model and the radius of ${}_{100}^{257}Fm$ is n times the Bohr radius, then the value of n is :

• A. 4
• B. $\frac{1}{4}$
• C. 200
• D. 100

Answer 1

Answer: (B)

$\frac{1}{4}$

According to Bohr's model

$r_m=\frac{m^2}{2}.r_0$

where, m is orbit number and $r_0$ is the Bohr's radius for ${}_{100}^{257}FM$,

$Z=100,m=5,r_m=n{r}_0$

$n{r}_0=\frac{5^2{r}_0}{100}$ or $n=\frac{1}{4}$