Question

If the radius of Bohr's first orbit is \( a_0 \), what is the radius of the \( n \)th orbit?

• A. \( n a_0 \)
• B. \( \dfrac{a_0}{n} \)
• C. \( n^2 a_0 \)
• D. \( \dfrac{a_0}{n^2} \)

Hint:

In Bohr's atomic model, the orbit radius grows as \( n^2 \), so higher orbits are much farther from the nucleus than lower ones.

Answer 1

The Correct Option is C

According to Bohr's model of the hydrogen atom, the radius of the \( n \)th orbit is given by: \[ r_n = n^2 a_0 \] where \( a_0 \) is the radius of the first orbit (Bohr radius) and \( n \) is the principal quantum number.
So, the radius of the \( n \)th orbit increases with the square of \( n \).