Understand the relationships for a hydrogen atom.

For a hydrogen atom, the velocity of an electron in an orbit is inversely proportional to the principal quantum number $n$, and the radius of the orbit is directly proportional to the square of the principal quantum number $n$.

Let the initial state be $n_1$ and the final state be $n_2$.
The electron is initially in the ground state, so $n_1 = 1$.
The initial radius is $r_1 = r$.
The initial velocity is $v_1$.
The final velocity is $v_2 = \frac{v_1}{2}$.
We need to find the final radius $r_2$.

From $v \propto \frac{1}{n}$, we have:

Substitute the given values:

So, the electron jumps to the second energy level.

From $r \propto n^2$, we have:

Substitute the known values:

The new radius will be $4r$.

The correct option is (b).