If the radius of the electron orbit for \( n = 3 \) for a hydrogen atom is \( 4.5\ \mathring{\mathrm{A}} \). The radius for \( n = 2 \) orbit is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2.0\ \mathring{\mathrm{A}} \)
In the Bohr model, the orbit radius is \( r_{n} = n^{2}a_{0}/Z \), so for the same atom the radius is proportional to the square of the orbit number.
\( \displaystyle \frac{r_{2}}{r_{3}} = \frac{2^{2}}{3^{2}} = \frac{4}{9} \)
\( \displaystyle r_{2} = \frac{4}{9}\times4.5\,\mathring{\mathrm{A}} = 2.0\,\mathring{\mathrm{A}} \)