Final answer:
The number of possible spectral lines that can be emitted in the Brackett series when transitioning from the 9th excited level to the ground state is 15, but if the question was meant for the Lyman series, the answer would be 36.
Step-by-step explanation:
The number of possible spectral lines that may be emitted in the Brackett series for a hydrogen atom when an electron transitions from the 9th excited level (n=10) back to the ground state is calculated using the formula for the total number of transitions N = ½(ni - nf) (ni - nf - 1), where ni is the initial energy level and nf is the final energy level.
Since the Brackett series involves transitions to the n=4 energy level, we calculate the number of lines that can be produced when an electron falls from the n=10 level to n=4, which is the initial energy level for this series. Therefore, N = ½(10 - 4)(10 - 4 - 1) = ½(6)(5) = 15. However, since the question specifically asked for transitions to the ground state (n=1), it seems there may be a confusion in the provided choices as they do not match the Brackett series values. If they meant transitions down to n=1, it would involve the Lyman series, and the calculation would be N = ½(10 - 1)(10 - 1 - 1) = ½(9)(8) = ¿36, which corresponds to choice (c).