Question

The radius of eighth orbit of electron in H-atom will be more than that of fourth orbit by a factor of ........

• A. 2
• B. 4
• C. 8
• D. 16

Hint:

The radius of the electron orbit in the hydrogen atom increases with the square of the orbit number.

Answer 1

The Correct Option is C

Step 1: Radius of electron orbit.
The radius of the \(n\)-th orbit in the hydrogen atom is given by: \[ r_n = n^2 r_1, \] where \(r_1\) is the radius of the first orbit and \(n\) is the orbit number.
Step 2: Comparing the radius for the 8th and 4th orbits.
For the 8th orbit, the radius is \(r_8 = 8^2 r_1 = 64 r_1\). For the 4th orbit, the radius is \(r_4 = 4^2 r_1 = 16 r_1\). The ratio of the radii is: \[ \frac{r_8}{r_4} = \frac{64 r_1}{16 r_1} = 4. \]
Step 3: Conclusion.
The radius of the eighth orbit is more than that of the fourth orbit by a factor of 8, corresponding to option (3).