___________ is a measure of the relative contributions of the orbital moment and the spin moment to the total magnetic moment.

Lande’s factor

Gibbs factor

Newton’s ratio

None of the mentioned

An electron in orbit around a nucleus gives rise to an effective current loop and thus an additional magnetic moment, but this effect is negligible compared to the magnetic moment due to spin. Lande’s factor is a relative measure of these orbital moments.

For a multi-electron atom $$l$$, L and S specify the one electron orbital angular momentum, total orbital angular momentum and total spin angular momentum respectively. The selection rules for electric dipole transition between the two electronic energy levels, specified by $$l$$, L and S are

ΔL = 0, ±1; ΔS = 0; Δ$$l$$ = 0, ±1

ΔL = 0, ±1; ΔS = 0; Δ$$l$$ = ±1

ΔL = 0, ±1; ΔS = ±1; Δ$$l$$ = 0, ±1

ΔL = 0, ±1; ΔS = ±1; Δ$$l$$ = ±1

The ratio of the orbital dipole moment to the orbital angular moment is given by

e/m

–e/m

e/2m

–e/2m

A system containing N non-interacting localized particles of spin $$\frac{1}{2}$$ and magnetic moment $$\mu $$ each is kept in constant external magnetic field B and in normal equilibrium at temperature T. The magnetization of the system is

$$N\mu \coth \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$

$$N\mu \tanh \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$

$$N\mu \sinh \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$

$$N\mu \cosh \left( {\frac{{\mu B}}{{{k_B}T}}} \right)$$

What is the difference in energy between two spin angular momentum states of a hydrogen atom in a 1s orbital, experiencing a magnetic field of 1 Tesla?

6.31 × 10-20J

1.59 × 10-15J

3.13 × 10-25J

1.86 × 10-23J

A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$ = Angular velocity of precession of the axis of spin)

$$\frac{1}{2}I{\omega ^2}$$

$$I{\omega ^2}$$

$$\frac{1}{2}I\omega \omega {\text{P}}$$

$$I\omega \omega {\text{P}}$$

An atom with net magnetic moment $$\overrightarrow \mu $$ and net angular momentum $$\overrightarrow {\bf{L}} \left( {\overrightarrow \mu = \gamma \overrightarrow {\bf{L}} } \right)$$ is kept in a uniform magnetic induction $$\overrightarrow {\bf{B}} = {B_0}{\bf{\hat k}}.$$ The magnetic moment $$\overrightarrow \mu \left( { = {\mu _x}} \right)$$ is

$$\frac{{{d^2}{\mu _x}}}{{d{t^2}}} + \gamma {B_0}{\mu _x} = 0$$

$$\frac{{{d^2}{\mu _x}}}{{d{t^2}}} + \gamma {B_0}\frac{{d{\mu _x}}}{{dt}} + {\mu _x} = 0$$

$$\frac{{{d^2}{\mu _x}}}{{d{t^2}}} + {\gamma ^2}B_0^2{\mu _x} = 0$$

$$\frac{{{d^2}{\mu _x}}}{{d{t^2}}} + 2\gamma {B_0}{\mu _x} = 0$$

Deuteron in its ground state has a total angular momentum J = 1 and a positive parity. The corresponding orbital angular momentum L and spin angular momentum S combinations are

L = 0, S = 1 and L = 2, S = 0

L = 0, S = 1 and L = 1, S = 1

L = 0, S = 1 and L = 2, S = 1

L = 1, S = 1 and L = 2, S = 1

How is the total angular momentum of a system J described in terms of spin angular momentum S and orbital angular momentum L?

J = L

J = L+S

J = 2πL + SBe$^{-\frac{\hbar^2}{2}}$

J = S2L

Two spin-1/2 fermions having spins $$\overrightarrow {{S_1}} $$ and $$\overrightarrow {{S_2}} $$ interact via a potential $$V\left( r \right) = \overrightarrow {{S_1}} .\overrightarrow {{S_2}} \,{V_0}\left( r \right).$$ The contributions of this potential in the singlet and triplet states, respectively are

$$ - \frac{3}{2}{V_0}\left( r \right){\text{ and }}\frac{1}{2}{V_0}\left( r \right)$$

$$\frac{1}{2}{V_0}\left( r \right){\text{ and }} - \frac{3}{2}{V_0}\left( r \right)$$

$$\frac{1}{4}{V_0}\left( r \right){\text{ and }} - \frac{3}{4}{V_0}\left( r \right)$$

$$ - \frac{3}{4}{V_0}\left( r \right){\text{ and }}\frac{1}{4}{V_0}\left( r \right)$$

In a two-electron atomic system having orbital and spin angular momenta $${l_1}{l_2}$$ and $${s_1}{s_2}$$ respectively, the coupling strengths are defined as $${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}},\,{\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}},\,{\Gamma _{{l_1}{l_2}}}$$ and $${\Gamma _{{l_2}{s_1}}}.$$ For the jj coupling. scheme to be applicable, the coupling strengths must satisfy the condition

$${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$

$${\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$

$${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$

$${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$