A large collection of hydrogen atoms is excited so that every atom is initially in the sixth Bohr orbit. The atoms are then allowed to de-excite, and every possible transition occurs somewhere in the sample. Find the maximum number of distinct spectral lines that can be observed.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
JEE Mains NEET JEE Advanced

Question

A large collection of hydrogen atoms is excited so that every atom is initially in the sixth Bohr orbit. The atoms are then allowed to de-excite, and every possible transition occurs somewhere in the sample. Find the maximum number of distinct spectral lines that can be observed.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

A large sample can realise every possible transition between the six available levels. The number of distinct pairs of levels is N(lines) = n(n−1) ÷ 2. For n = 6: N(lines) = 6×5 ÷ 2 = 15. Hence the maximum number of distinct spectral lines is 15.