Question

Given that the radius of the first Bohr orbit of hydrogen atom is 53 pm, the radius of its third Bohr orbit is ................ pm. (Round off to the nearest integer)

Hint:

The radius of the Bohr orbit increases with the square of the principal quantum number: \(r_n = n^2 \times r_1\).

Answer 1

Correct Answer: 477

Step 1: Formula for the radius of Bohr orbit.
The radius \(r_n\) of the \(n^{th}\) Bohr orbit for hydrogen atom is given by the formula: \[ r_n = n^2 \times r_1 \] where \(n\) is the principal quantum number and \(r_1\) is the radius of the first Bohr orbit.
Step 2: Calculate the radius for the third Bohr orbit.
For the third Bohr orbit (\(n = 3\)) and \(r_1 = 53 \, \text{pm}\): \[ r_3 = 3^2 \times 53 = 9 \times 53 = 477 \, \text{pm} \] Thus, the radius of the third Bohr orbit is 159 pm.