Modern Physics

 Mass defect, packing fraction and binding energy: It was assumed that mass of the nucleus is equal to the mass of its constituents (i.e protons and neutrons). But experimentally it was found that the actual mass of the nucleus is less than the theoretical mass. Thus, the difference between the theoretical mass and experimental mass is called mass defect i.e ∆m={[Zmₚ + (A-Z)mₙ] - M} Where mₚ= mass of proton              mₙ= mass of neutron               M= actual mass of nucleus                Z= atomic number                A= mass number The ratio of mass defect and mass number (A) is called packing fraction (f) f = ∆m/A Thus packing fraction is the mass defect available per nucleon. The packing fraction explains the stability of the nucleus. The packing fraction may be positive, negative or zero. The positive value of packing fraction indicates that the nuclei is unstable while the negative value of packing fraction indicates that a fraction of nucleus mass has been converted into e

 Nuclear charge; The nucleus consist of protons and neutrons. Since neutrons do not have any charge, thus the nuclear charge is equal to the integral multiple of proton charge i.e Ze where Z is the number of protons inside the nucleus. In 1914, Mosley determined the nuclear charge during the study of wavelength of X-ray emitted from different elements. Since the atom is electrically neutral, it can be explained that atomic number X represents the number of electrons outside the nucleus and is equal to number of protons inside the nucleus and the sum of number of protons and neutrons inside the nucleus is called mass number A. Thus the number of neutrons inside the nucleus i.e N=A-Z. Nuclear mass; Almost the entire mass of an atom (~99.75%) is concentrated in the nucleus. Nuclear mass is obtained by subtracting electrons mass from atomic mass. Nuclear mass is not exactly equal to the integral multiple of standard atomic mass unit except ¹²C₆. But the nuclear mass is nearly equal to the

 The Vibrational Rotational spectra; Since the vibrational and rotational energies of diatomic molecules are different. The rotation of molecule does not affect its vibrational motion. Total energy of molecule. Total energy of molecule. R branch; When transition occurs such that ∆𝝂 = +1, ∆j = +1. This branch of spectrum is called R branch. Q branch; When transition occurs such that ∆𝝂 = +1, ∆j = 0. This branch of the spectrum is called Q branch and this type of transition is not allowed in diatomic molecule. P branch; When transition occurs, such that ∆𝝂 = +1, ∆j = -1. This branch of the spectrum is called P branch. Rotation Vibration transition.

 Vibrational Spectra; The selection rule followed by vibration transition is ∆𝛎 = ± 1 (+ve is for absorption and -ve is for emission). The energy of vibration transition from lower level denoted by 𝛎 to upper level denoted by (𝛎+1) is given by Transition rule for vibrational spectra.   Thus the pure vibrational Spectra will consist of single line as shown in fig. The frequency of spectral line is equal to classical frequency and is independent of vibrational quantum number i.e 𝛎. Pure vibrational Spectra. The homonuclear diatomic molecule such as H₂ ,O₂ ,N₂ have zero dipole moment, thus does not exhibit vibrational spectra, while the heteronuclear diatomic molecule such as HCl, HBr, HF, HCN etc have dipole moment, thus exhibit vibrational spectra.

 Vibrational energy level; Vibrational energy level. Vibrational energy level.

 Rotational spectrum Rotational spectrum. Rotational spectrum.

 Quantisation of rotational energies Quantisation of rotational energies. Quantisation of rotational energies.

 Lande g factor Lande g factor Lande g factor.

 Anormalous Zeeman effect and Paschen Back Effect. Anormalous Zeeman effect. Anormalous Zeeman effect and Paschen Back Effect.

 Normal Zeeman effect; Normal Zeeman effect. Normal Zeeman effect.