B

Step 1: According to Bohr's model, the time period T of the electron in the nth orbit is given by:
$$T_n = rac{2\pi n^3}{k}$$
where k is a constant.
Step 2: Given that the time period in the initial state (n1) is eight times that in the final state (n2), we can write the equation as:
$$T_{n_1} = 8 T_{n_2}$$
Substitute the expressions for the time periods:
$$\frac{2\pi n_1^3}{k} = 8 \frac{2\pi n_2^3}{k}$$
The constants cancel out, leading to:
$$n_1^3 = 8 n_2^3$$
Step 3: Taking the cube root of both sides gives:
$$n_1 = 2 n_2$$
Step 4: Now, substituting possible integer values for n2:
- If n2 = 1, then n1 = 2 * 1 = 2
- If n2 = 2, then n1 = 2 * 2 = 4
- If n2 = 3, then n1 = 2 * 3 = 6
Step 5: Thus, the valid pairs of (n1, n2) can be (2, 1), (4, 2), (6, 3), etc.
Hence, the possible values according to the options would be (4, 2).
Therefore, the answer is (n1, n2) = (4, 2).