Electronic Transitions in the Hydrogen Atom Using Figure predict which of these electronic transitions produces the spectral line having the longest wavelength: n = 2 to n=1,n = 3 to n = 2, or n = 4 to n = 3. ? Figure Energy levels in the hydrogen atom from the Bohr model. The arrows refer to the transitions of the electron from one allowed energy state to another. The states shown are those for which n = 1 through n = 6 and the state for n = °° for which the energy, E, equals zero. For each of the following transitions, give the sign of AE and indicate whether a photon is emitted or absorbed: (a) n = 3 to n = 1; (b) n = 2 to n = 4.
Solution: Here, we are going to determine the sign of E for the given transitions and also indicate whether a photon is emitted or absorbed. Step1: The spectrum of hydrogen atom has played a very important role in the development of atomic structure. It can be obtained by passing an electric discharge through the gas taken in the discharge tube under low pressure. The emitted light is analysed with the help of spectroscope. The spectrum consists of a large number of lines appearing in different regions of wavelengths. The line spectrum observed in case of hydrogen atom can be quantitatively explained using Bohr’s model. When an electron jumps from a lower orbit to a higher orbit, it absorbs energy. When the electron jumps from higher orbit to lower orbit, it emits energy. The amount of energy absorbed or emitted when an electron jumps from orbit n(initial orbit) to i orbit n(fifl orbit) may be given as: --------(1) Step2: 2 2 In case of absorption spectrum, i.e., n > n, the term [(1/nf - i/n )] becomes negativefo that i E is positive and hence energy is absorbed. In case of emission spectrum, i.e., n > n, the term [(1/i ) -f1/n )] becomes positive f that E i is negative and hence energy is emitted. Step3: a) For the transition, n = 3 to n = i n > n andf nce E ii egafve. Since, the transition is from higher energy level to lower energy level, therefore, photon is emitted. b) For the transition, n = 2 to n = 4, n < n and hence E is positive. Since, the transition is i f i f from lower energy level to higher energy level, therefore, photon is absorbed. ------------------