Question

The radius of the third stationary orbit of an electron in Bohr's atom is $R$. The radius of the fourth stationary orbit will be:

• A. $\frac{4}{3} R$
• B. $\frac{16}{9} R$
• C. $\frac{3}{4} R$
• D. $\frac{9}{16} R$

Answer 1

Answer: (B)

$\frac{16}{9} R$

Answer 2

According to Bohr’s theory, the radius of an electron’s orbit is given by:

$r \propto \frac{n^2}{Z}$

where $n$ is the principal quantum number and $Z$ is the atomic number. Since the electron is in hydrogen ($Z = 1$), we get:

$\frac{r_4}{r_3} = \frac{4^2}{3^2} = \frac{16}{9}$

Thus, $r_4 = \frac{16}{9}R$.