1. Interpret the question

   Atomic hydrogen is initially in the 4th energy level, i.e. $n=4$.

   When the electron de-excites to lower levels, it can emit photons corresponding to all possible transitions among the levels involved.

2. Levels involved

   Since the atom is in the 4th level, the possible lower levels are: $n=4,3,2,1$

3. Count all possible emitted spectral lines

   Each spectral line corresponds to one possible transition from a higher level to a lower level.

   The total number of distinct transitions among $n$ levels is: $N = \frac{n(n-1)}{2}$

   Here $n=4$, so: $N = \frac{4(4-1)}{2} = \frac{4\cdot 3}{2} = 6$

4. List the transitions explicitly

   The 6 possible transitions are:

   • $4 \to 3$
   • $4 \to 2$
   • $4 \to 1$
   • $3 \to 2$
   • $3 \to 1$
   • $2 \to 1$

   Hence, the number of spectral lines emitted is 6.

5. Check the options

   • A: 3 ❌
   • B: 6 ✅
   • C: 1 ❌
   • D: 0 ❌

Final Answer: Option B