A sample of hydrogen-like atoms in a specific excited state emits exactly 3 distinct spectral lines. If the longest and shortest wavelengths among these lines are _L and _S respectively, the wavelength of the third spectral line is

Step-by-step solution

The number of distinct spectral lines emitted by a sample of atoms in the n^ th state is given by n(n-1) 2 . Given that 3 lines are emitted, n(n-1) 2 = 3 n = 3 . The possible transitions are from n=3 to n=1 , n=3 to n=2 , and n=2 to n=1 . The energy of a transition is inversely proportional to its wavelength ( E = hc ). The transition with the maximum energy ( n=3 to n=1 ) will have the shortest wavelength, so ₃₁ = _S . The transition with the minimum energy ( n=3 to n=2 ) will have the longest wavelength, so ₃₂ =