Question

If an orbital electron of the hydrogen atom jumps from the ground state to a higher energy state, its orbital speed reduces to half its initial value. If the radius of the electron orbit in the ground state is r, then the radius of the new orbit would be

• A. 2r
• B. 4r
• C. 8r
• D. 16r

Answer 1

The correct option is B 4r

We know that, orbital speed, $v_0\propto \frac{1}{n}$
As orbital speed is reduced to half the initial value, $n=2$
Now, radius, $r_n\propto n^2$
Hence, the radius of the new orbit $=(2{)}^2\times r=4r$ and the correct choice is (b).