Question

Explain:

a) The similarity between the electron and the X-ray diffraction patterns of aluminium.
b) The line in the hydrogen atom spectrum splits into two when placed in a magnetic field.
c) The appearance of coloured lines for H atom in the Balmer series while the Lyman series can only be observed with an ultraviolet lamp.

Answer 1

(a) The earlier electron-diffraction were carried out using a thin polycrystalline metallic foil as a target, which was similar to the techniques used to study the x-ray diffraction. The similarity between these experiments is that the beam passes through the target rather than being reflected from it.

X-Ray and Electron diffraction patterns of the Aluminium foil are shown. The upper half of the photo shows the diffraction pattern for 71-pm x-rays passing through aluminium foil. The lower half, with a different scale, shows the diffraction pattern for 600 eV electrons from Aluminium. The similarity shows that electrons undergo the same kind of diffraction as x rays.

(b)Zeeman observed that when a light -source giving line spectrum is placed in an external magnetic field, the psectral lines emiited by the atoms of the source are split into a number of polarised components. this splitting is attributed to the interaction between the magnetic field and the magnetic dipole moment associated with the orbital angular momentum.

The Normal Zeeman Effect which is shown by all lines due to transition between the singlet(S=0) states of an atom can be explained from the classical electron theory and also from the quantum theory without taking note of electron spin.

(c)The Balmer series is characterized by the electron transitioning from n>= 3 to n=2, where n refers to principal quantum number of the electron. as the first spectral lines associated with this series are located in the visible part of the electromagnetic spectrum. Angstrom has measured the four visile spectral lines to have wavelengths 656.21, 486.07, 434.01 and 410.12 nm which corresponds to Red, Teal, Blue, and Indigo colors.

The version of he Formula that generated lyman and Balmer series is

1/ wavelength (in lambda) = RH ( 1- 1/n²  ) ; R_H   is the Rydberg Formula.

Lymann series is a hydrogen spectral series of transitions of the hydrogen atom as an electron goes from n>=2 to n=1 (where n is the principal quantum number, the lowest energy level of the spectrum. The wavelenths of lyman series obtained from this formula lies in the ultravoilet regions therefore we need a ultravoilet lamp to view them.