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

A

J = L

B

J = L+S

C

J = 2πL + SBe\(^{-\frac{\hbar^2}{2}}\)

D

J = S2L

Correct Answer: J = L+S

Total angular momentum is just a vector sum of spin angular momentum and orbital angular momentum. This leads to a phenomenon called spin-orbit coupling that contributes to the total Hamiltonian of a system. In this case, total angular momentum of the atomic system is described in this way.

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

A

ΔL = 0, ±1; ΔS = 0; Δ$$l$$ = 0, ±1

B

ΔL = 0, ±1; ΔS = 0; Δ$$l$$ = ±1

C

ΔL = 0, ±1; ΔS = ±1; Δ$$l$$ = 0, ±1

D

ΔL = 0, ±1; ΔS = ±1; Δ$$l$$ = ±1

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

A

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

B

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

C

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

D

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

An atom with one outer electron having orbital angular momentum $$l$$ is placed in a weak magnetic field. The number of energy levels into which the higher total angular momentum state splits, is

A

2$$l$$ + 2

B

2$$l$$ + 1

C

2$$l$$

D

2$$l$$ - 1

If an atom is in the ³d₃ state, the angle between its orbital and spin angular momentum vectors ($$\overrightarrow {\bf{L}} $$ and $$\overrightarrow {\bf{S}} $$) is

A

$${\cos ^{ - 1}}\frac{1}{{\sqrt 3 }}$$

B

$${\cos ^{ - 1}}\frac{2}{{\sqrt 3 }}$$

C

$${\cos ^{ - 1}}\frac{1}{2}$$

D

$${\cos ^{ - 1}}\frac{{\sqrt 3 }}{2}$$

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)

A

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

B

$$I{\omega ^2}$$

C

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

D

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

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?

A

6.31 × 10-20J

B

1.59 × 10-15J

C

3.13 × 10-25J

D

1.86 × 10-23J

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

A

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

B

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

C

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

D

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

What is the change in the angular momentum of a system as per the Law of Conservation of Angular momentum, if the total external torque acting is zero?

A

Remains constant

B

Becomes zero

C

Increases exponentially

D

None of the above

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

A

e/m

B

–e/m

C

e/2m

D

–e/2m

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

A

Lande’s factor

B

Gibbs factor

C

Newton’s ratio

D

None of the mentioned