A sample of hydrogen atoms in a higher excited state n emits exactly 6 different wavelengths of light when de-exciting to the ground state. If _ max is the longest wavelength and _ min is the shortest wavelength among all the emitted spectral lines, the ratio _ max _ min is

Step-by-step solution

The number of spectral lines emitted when electrons de-excite from the n^ th state to the ground state is given by n(n-1) 2 . n(n-1) 2 = 6 n^2 - n - 12 = 0 n = 4 The shortest wavelength _ min corresponds to the transition with the maximum energy, which is from n = 4 to n = 1 . 1 _ min = R ( 1 1^2 - 1 4^2 ) = R (1 - 1 16 ) = 15R 16 _ min = 16 15R The longest wavelength _ max corresponds to the transition with the minimum energy among all possible transitions. The energy difference between adjacent levels decreases a