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

Electric Current in Atoms - Bohr Magneton ; magnetic moment of electron in orbit

The revolution of electron in its orbit around nucleus resembles a magnetic dipole and the magnetic moment due to this orbital motion of electron is

𝜇ₑ₁ = - (e/2m) x angular momentum

angular momentum = mr²w

The minus sign indicates that dipole moment points in direction opposite to vector representing angular momentum.

The ratio of magnetic dipole moment of the electron due to its orbital motion and angular momentum of orbital motion is called "orbital gyro magnetic ratio" represented by '𝛾'.

𝛾 = (magnetic moment/angular momentum) = e/2m

The strength of magnetic dipole is given by

 𝜇ₑ₁ = -𝜇B.l;  

𝜇B - Bohr Magneton = (eh/4πm) = 9.27 x 10⁻²⁴ Amp.m²

Therefore, '𝜇B'  represents magnetic moment of an elementary permanent magnetic dipole.

As we know that for a 'l' value there exists a quantum number 'ml' such that it takes +l to -l values hence for a d-electron for eg:

corresponding possible magnetic moment along direction of field are 2𝜇B, 𝜇B, 0, -𝜇B, -2𝜇B

 Therefore  𝜇ₑ₁ = -𝜇B.ml