Question

If the radius of the 3rd Bohr's orbit of hydrogen atom is r3 and the radius of 4th Bohr's orbit is r4. Then

• A. $r_4=\frac{9}{16}r_3$
• B. $r_4=\frac{16}{9}r_3$
• C. $r_4=\frac{3}{4}r_3$
• D. $r_4=\frac{4}{3}r_3$

Answer 1

Answer: (B)

$r_4=\frac{16}{9}r_3$

Answer 2

$r_n =r_0 \frac{n^2}{z}$

$r^4 = r_0 \times \frac{4^2}{1}$ and

$r^3 = r_0 \times \frac{3^2}{1}$

Therefore, $\frac{r^4}{r^3} = \frac{4^{\frac{2}{3}}}{2} i.e,r^4 = \frac{16}{9}r^3$