Question

If we apply the Bohr model to a ${}_{100}^{257}Fm$ atom, its radius in units of the Bohr radius is obtained as

• A. $257$
• B. $100$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

The correct option is D $\frac{1}{4}$

Given :If we apply the Bohr model to a

${}_{100}^{257}Fm$ atom, its radius in units of the Bohr radius is obtained as

Solution :

For an atom following Bohr’s model, the radius is given by

$r_m=\frac{r_o{m}^2}{Z}$

$r_o$ = Bohr’s radius and m = orbit number.

For Fm, m = 5 (Fifth orbit in which the outermost electron is present)

$r_o=\frac{5^2{r}_o}{100}$= $r_{o}n$

$n=\frac{1}{4}$

The Correct Opt = D