Modern Physics - Graduate level important notes for competitive exams - PART2

•  4n series is called as "Thorium" series.

• 4n+1 series is called as "Neptunium" series.

• 4n+2 series is called as "Uranium" series

• 4n+3 series is called as "Actinium" series

• X-rays & 𝛾-rays of same energies are distinguished by their frequencies

• Spin of a Deuteron  is 1.

• Spin of Muons is 1/2.

• Spin of Pions (π-mesons) is zero.

• Spin of Photon is 1.

• Spin of Graviton is 2.

• Mass of a Proton is 1.0072766 amu

• Mass of a Neutron is 1.0086654 amu

• The total quantum number 'n' specified "Energy" quantization.

• The azimuthal quantum number specified "Angular Momentum".

• The magnetic moment of proton is given by 2.8eħ/2mp

• The magnetic moment of Neutron is given by 1.9eħ/2mp.

• In Davisson-Germer experiment , the angle between incident beam and diffracted beam is called "co-lattitude".

• In heavy atoms the spin-orbit interaction is almost equal to "electrostatic interaction".

• L-S coupling is due to "electrostatic interaction".

• L-S coupling scheme breaks down in strong magnetic field and applies to light atoms.

• In light atoms, "orbit interaction" is less than "electrostatic interaction".

• According to shell model nucleons interact primarily with a general force field rather than directly with one another.

• Magic numbers: 2,8,20,28,50,82,126

• Debroglie wavelength associated with electron accelerated to a potential V is ƛ=12.26/√V A⁰

REFRIGERATION - IMPORTANT NOTES

Refrigerating machines are of two types 1) Vapour compression machine (Frigidaire)" and 2) "Vapour absorption machine". 

Refrigerant: 

The liquid which on evaporation produces cooling is called refrigerant. Some examples are Ammonia(NH₃), Sulphur dioxide, Freon.

Properties of Refrigerant:

1. It should have low boiling point & melting point
2. It should be vapor at normal temperature and pressure.
3. It should have high thermal conductivity
4. "Latent heat of vaporization" of the refrigerant must be large.  
5.  The specific volume should be small in order to reduce the size of compressors. 

The evaporation of liquid under reduced pressure is a cooling process. The reason is that when a substance changes from liquid to vapor phase, it is associated with absorption of heat. If this heat is not taken from any external source, the necessary heat for phase exchange is taken from itself which therefore cools.

Vapor Compression Machine

Production of temperature by making a liquid evaporate rapidly under reduced pressure and circulating evaporating liquid around enclosure.

Debye's theory of Atomic Heat Capacity of Solids - Important Notes

 The failure in Einsteins theory of specific heat at low temperature is due to assumption that the vibrations of all atoms are simple harmonic and have one and same frequency.

"Debye" improved the Einsteins theory by considering the atomic oscillators as a system of coupled oscillators having a continuous range of frequencies.

Essential difference between Debye & Einstein model:

Debye has considered the vibrational modes of a crystal as a whole, where as Einstein has considered the vibration of a single atom with the assumption that atomic vibrations are independent of each other.   

Debye has made following assumptions:

1. The solid is capable of vibrating elastically in many different modes.
2. The frequency of vibration is different for different modes.
3. The number of modes of vibration of waves solids are limited in number.
4. The maximum frequency is the fundamental frequency of solid. The maximum frequency is frequency of shorter waves which the solid can transmit. 

According to Debye, a solid can be treated as an elastic body in which vibrations of atoms generate "stationary waves" of both longitudinal & transverse types with velocities Vl & Vt respectively.

The velocities can be determined by elastic constants & densities of solids.

The frequencies range from zero to a definite upper limit.

The number of modes of longitudinal waves per unit volume with frequencies between '𝝂' & '𝝂+d𝝂 ' is represented by 4Π𝝂²d𝝂/(Vl)³.

The number of modes of transverse vibrations per unit volume with frequencies between '𝝂' & '𝝂+d𝝂 ' is represented by 8Π𝝂²d𝝂/(Vt)³. Here 8Π is taken in place of 4Π. Because transverse vibrations have two independent directions of vibration i.e. they are equivalent to two waves at right angles to each other.

So total number of modes of vibrations per unit volume with frequencies '𝝂' & '𝝂+d𝝂 ' is given by  

4Π[(1/Vl³)+(2/Vt³)]𝝂²d𝝂

The total number of independent modes of vibrations is given by  

4ΠV[(1/Vl³)+(2/Vt³)] ∫𝝂²d𝝂 ; V is volume of gm-mole of solid

Why U-235, as isotope of Uranium with only 0.7% abundance will undergo fission if it captures a thermal Neutron where as U-238 will not?

 From 'B/A' against A curve, we know that Binding Energy per Nucleon in Uranium region is about 7MeV, which is almost equal to height of potential barrier opposing fission. 

Now,U-238.in  when a Neutron is added to Nucleus of ₉₂U²³⁵, we get ₉₂U²³⁶ i.e. an Even-Even nuclide. The pairing term in mass formula for Uranium is about 0.6MeV. Thus, we see that Thermal Neutron capture in U-235 results in total energy release of 7.6 MeV and since to cross potential barrier, only about 7 MeV is required. So U-235 can undergo fission by Thermal Neutron capture.

On the other hand, U-238 nucleus, after Neutron capture becomes a U-239 nucleus which is an Even-Odd Nuclide. Due to absence of pairing term for U-239, the fission barrier cannot be crossed. So Thermal Neutrons will not induce fission.        

Useful Range of Materials for Vacuum Vessels and Pipes