For an electron in hydrogen atom, the states are characterized by the usual quantum numbers n, $$l$$, m$$l$$. The electric dipole transition between any two states requires that

Δ$$l$$ = 0, Δm$$l$$ = 0, ±1

Δ$$l$$ = ±1, Δm$$l$$ = ±1, ±2

Δ$$l$$ = ±1, Δm$$l$$ = 0, ±1

Δ$$l$$ = ±1, Δm$$l$$ = 0, ±2

Correct Answer: Δ$$l$$ = ±1, Δm$$l$$ = 0, ±1

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

Consider the following statements:
1. The Supreme Court has original jurisdiction in any dispute between the Government of India and one or more States.
2. The Supreme Court has original jurisdiction in any dispute between the Government of India and any State or States on one side and one or more other State on the other.
3. The Supreme Court has original jurisdiction in any dispute between the Government of India and any corporation of Individual one side and one or more States on the other.
4. The Supreme Court has original jurisdiction in any dispute between two or more States.
Which of these statements are correct?

1 and 2

1, 2 and 4

3 and 4 only

1, 2, 3 and 4

Two states of an atom have definite parities. An electric dipole transition between these states is

allowed if both the states have even parities

allowed if both the states have odd parities

allowed if the two states have opposite parities

not allowed unless a static electric field is applied

A magnetic dipole of dipole moment $$\overrightarrow {\bf{m}} $$ is placed in a non-uniform magnetic field $$\overrightarrow {\bf{B}} .$$ If the position vector of the dipole is $$\overrightarrow {\bf{r}} ,$$ the torque acting on the dipole about the origin is

$$\overrightarrow {\bf{r}} \times \left( {\overrightarrow {\bf{m}} \times \overrightarrow {\bf{B}} } \right)$$

$$\overrightarrow {\bf{r}} \times \overrightarrow \nabla \left( {\overrightarrow {\bf{m}} .\overrightarrow {\bf{B}} } \right)$$

$$\overrightarrow {\bf{m}} \times \overrightarrow {\bf{B}} $$

$$\overrightarrow {\bf{m}} \times \overrightarrow {\bf{B}} + \overrightarrow {\bf{r}} \times \overrightarrow \nabla \left( {\overrightarrow {\bf{m}} .\overrightarrow {\bf{B}} } \right)$$

Mr A started half an hour later than usual for the marketplace. But by increasing his speed to $$\frac{3}{2}$$ times his usual speed he reached 10 minutes earlier than usual. What is his usual time for this journey?

1 hours

2 hours

3 hours

45 minutes

None of these

There are only three bound states for a particle of mass m in a one-dimensional potential well of the form shown in the figure. The depth V₀ of the potential satisfies

[ A. $$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}} B. $$\frac{{{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

$$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

The binding energy of an electron to a proton (i.e., hydrogen atom) is 13.6 eV. The loss of mass in the formation of one atom of hydrogen is _____________

2.42 X 10-35 Kg

3.34 X 10-35 Kg

4.58 X 10-35 Kg

5.19 X 10-35 Kg

An electric dipole will be in stable equilibrium if the angle between the axis of the dipole and the electric field is ________

0 degree

180 degree

90 degree

45 degree

An oxygen atom produced a dipole moment of 5 X 10-23 cm when subjected to an electric field. If the separation between the center of electronic cloud and the nucleus is 4 X 10-17 m, what is the polarizability of the oxygen atom?

1.4 X 10-47 Fm2

1.7 X 10-47 Fm2

1.8 X 10-47 Fm2

1.9 X 10-47 Fm2

If an electric dipole is placed in a uniform electric field ______ will act on the dipole.

A force but no torque

Both force and torque

Torque but no force

No torque or force