If the atom $$_{100}F{m^{257}}$$ follows the Bohr model and the radius of $$_{100}F{m^{257}}$$ is $$n$$ times the Bohr radius, then find $$n.$$
A.
100
B.
200
C.
4
D.
$$\frac{1}{4}$$
Answer :
$$\frac{1}{4}$$
Solution : KEY CONCEPT : For an atom following Bohr’s model, the radius is given by
$${r_m} = \frac{{{r_0}{m^2}}}{Z}$$ where $${r_0}$$ = Bohr’s radius and $$m$$ = orbit number.
For $$Fm,m = 5$$ (Fifth orbit in which the outermost electron is present)
$$\therefore {r_m} = \frac{{{r_0}{5^2}}}{{100}} = n{r_0}\left( {{\text{given}}} \right) \Rightarrow n = \frac{1}{4}$$
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