Question

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

• A. Radius of 3rd orbit is nine times larger than that of 1st orbit.
• B. Radius of 8th orbit is four times larger than that of 4th orbit.
• C. Radius of 6th orbit is three times larger than that of 4th orbit.
• D. Radius of 4th orbit is four times larger than that of 2nd orbit.

Hint:

For Bohr's model, the radius of each orbit increases with the square of the principal quantum number \( n \). Thus, radius comparisons can be calculated using the formula \( r \propto n^2 \).

Answer 1

The Correct Option is C

We know that for Bohr’s model: \[ r \propto n^2 \] Where \( n \) is the principal quantum number. Hence, we have: \[ \frac{r_3}{r_1} = \left(\frac{3}{1}\right)^2 = 9, \quad \frac{r_8}{r_4} = \left(\frac{8}{4}\right)^2 = 4, \quad \frac{r_6}{r_4} = \left(\frac{6}{4}\right)^2 = 2.25, \quad \frac{r_4}{r_2} = \left(\frac{4}{2}\right)^2 = 4 \] Thus, the incorrect statement is option (3).