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

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

Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?

A

One

B

Two

C

Three

D

Four

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

Two splits A and B are ventilated from an intake airway. Resistances of the splits are 0.5 Ns²m^-8 and 0.8 Ns²m^-8 respectively. A regulator is placed in split B to maintain a flow of 15 m³/s and 10 m³/s in splits A and B respectively as shown in the figure. The size of the regulator in m² is

A

2.1

B

1.3

C

1.2

D

1.13

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

Which of the following statements is not true about a splitting rule at internal nodes of the tree based on thresholding the value of a single feature? , where i ∈ is the index of the relevant feature b) It move to the right or left child of the node on the basis of 1, where ϑ ∈ R is the threshold c) Here a decision tree splits the instance space, X = Rd, into cells, where each leaf of the tree corresponds to one cell d) Splits based on thresholding the value of a single feature are also known as multivariate splits

A

It move to the right or left child of the node on the basis of 1, where i ∈ is the index of the relevant feature

B

xi < ϑ

C

xi < ϑ

D

xi < ϑ

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

A

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

B

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

C

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

D

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

A piece of paraffin is placed in a uniform magnetic field H₀. The sample contains hydrogen nuclei of mass m_p, which interact only with external magnetic field. An additional oscillating magnetic field is applied to observe resonance absorption. If g₁ is the g-factor of the hydrogen nucleus, the frequency at which resonance absorption takes place, is given by

A

$$\frac{{3{g_1}e{H_0}}}{{2\pi {m_p}}}$$

B

$$\frac{{3{g_1}e{H_0}}}{{4\pi {m_p}}}$$

C

$$\frac{{{g_1}e{H_0}}}{{2\pi {m_p}}}$$

D

$$\frac{{{g_1}e{H_0}}}{{4\pi {m_p}}}$$

Find the velocity of an electron when its kinetic energy is equal to one electron volt (in 105m/s). Given charge of an electron e = 1.6 x 10-19 and mass of an electron m = 9.1 x 10-31.

A

3.9

B

4.9

C

5.9

D

6.9