Question

If the radius of first Bohr's orbit in a hydrogen atom is x $\stackrel{\circ }{A}$, then the radius of the third orbit in the hydrogen atom would be:

• A. 6x $\stackrel{\circ }{A}$
• B. 4x $\stackrel{\circ }{A}$
• C. 16x $\stackrel{\circ }{A}$
• D. 9x $\stackrel{\circ }{A}$

Answer 1

The correct option is D 9x $\stackrel{\circ }{A}$

Bohr's radius for $n^{th}$ orbit, $r_n=0.529\left[\frac{n^2}{Z}\right]\stackrel{\circ }{A}$
where, $n=\text{Energy level},Z=\text{Atomic number}$

For $H$ atom: $n=1,Z=1$
$r_H=0.529\left[\frac{1^2}{1}\right]\stackrel{\circ }{A}$ = 0.529 $\stackrel{\circ }{A}$ = x $\stackrel{\circ }{A}$
So, for third Bohr's orbit n = 3
$\therefore$ $r_n$ = $x\times \left(3^2\right)$ = 9x $\stackrel{\circ }{A}$