Quiz 28: Atomic Physics

Physics & Astronomy

No. The energy associated with the electron when it is located in a given state is given as follows: img Here, n is the principal quantum number, it represents the state in which the electron locates. From the above equation it is clear that the energy associated with the electron is inversely proportional to the square of the principal quantum number. Thus, as the n approaches to infinity, the energy of the electron will increase slightly by a finite amount. As the electron transition is possible between bound states only, the energy loss is always less than the ionization energy and hence the frequency of the emitted photon is always finite irrespective of the state of the electron.

The Lyman series of hydrogen spectrum is observed when the electron transition takes place from high energy states to the ground state of the atom. The reciprocal of the wavelength associated with different transitions in Lyman series is given as follows: img …… (1) Here, img is the wavelength of the radiation emitted during the transition, img is the Rydberg constant, and n is the principal quantum number. (a) The first line of the series is observed when the electron transition takes place from img to the ground state. Thus, equation (1) takes the following form. img Rearrange above equation for img . img Substitute img for img . img Therefore, the wavelength of the first line of the Lyman series is img . The second line of the series is observed when the electron transition takes place from img to the ground state. Thus, equation (1) takes the following form. img Rearrange above equation for img . img Substitute img for img . img Therefore, the wavelength of the second line of the Lyman series is img . The third line of the series is observed when the electron transition takes place from img to the ground state. Thus, equation (1) takes the following form. img Rearrange above equation for img . img Substitute img for img . img Therefore, the wavelength of the third line of the Lyman series is img . (b) Comparing the calculated wavelengths in part (a) with the wavelengths in standard electromagnetic spectrum one can conclude that the Lyman series is observed in far ultraviolet region.

The differences in the energies of the allowed states of the neon atom are responsible for the emission of photons with specific wavelengths that are responsible of the color of the sign. Since the wavelengths of the emitted photons are not continuous, neon signs do not emit continuous spectrum.