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

For Bohr’s model, the relationship \(r \propto n^2\) holds, where \(n\) is the principal quantum number. Applying this, we find:\[r_3/r_1 = (3/1)^2 = 9, \quad r_8/r_4 = (8/4)^2 = 4, \quad r_6/r_4 = (6/4)^2 = 2.25, \quad r_4/r_2 = (4/2)^2 = 4\]Therefore, the incorrect statement is option (3).