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

The Correct Option is B

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, \(r_4 = \frac{16}{9}R\).