Explanation

When a dipole with dipole moment $vec{p}$ is placed in an external electric field $vec{E}$, the torque experienced by the dipole is given by:

$$vec{tau} = vec{p} times vec{E}$$

This is a vector cross product, so:

• The magnitude is $tau = pE sintheta$

• The direction is perpendicular to both p​ and E (using the right-hand rule)

Explanation

 Andre-Marie Ampere discovered that a current-carrying conductor experiences a force when placed in a magnetic field.

This forms the basis of electromagnetism and is the principle behind electric motors.

Explanation

A Bloch wave represents the motion of an electron in a periodic potential. 

Bloch's theorem describes the wavefunction of electrons in a periodic potential, meaning the potential repeats itself regularly throughout the crystal lattice.

The wavefunction of a Bloch electron is then a product of a plane wave and a periodic function with the same periodicity as the potential. 

Explanation

If an electron has zero orbital angular momentum, its magnetic dipole moment also equals zero

This is because the magnetic dipole moment is directly proportional to the orbital angular momentum, and when the angular momentum is zero, the magnetic moment is also zero. 

Explanation

In semiconductors, as the temperature increases, more electrons gain enough energy to jump from the valence band to the conduction band.

This increase in free charge carriers results in higher electrical conductivity.

This is opposite to metals, where conductivity decreases with temperature due to increased scattering of electrons.

Explanation

 A space lattice (or crystal lattice) is a three-dimensional array of points arranged in a regular pattern, where each point has identical surroundings.

These points represent the positions of atoms, ions, or molecules in a crystal.

Unit cell: The smallest repeating unit of the lattice that, when repeated in space, builds the entire crystal.

Lattice points: Individual points in the lattice where atoms or molecules can be located.

Motif: The group of atoms associated with each lattice point.

Explanation

The energy gap (also called band gap) is the energy difference between the valence band (where electrons are bound) and the conduction band (where electrons are free to move).

• In conductors, the band gap is zero or overlaps.

• In semiconductors, the band gap is around 1 eV (e.g., silicon ≈ 1.1 eV).

• In insulators: The band gap is large, typically greater than 3 eV, and often around 5 eV or more.

This large gap in insulators prevents electrons from moving to the conduction band, making them poor conductors of electricity

Explanation

The Pauli exclusion principle applies to fermions, which have half-integer spin quantum numbers.

Option c) states "all particles with spin quantum numbers of '1/2', which is a half-integer.

Explanation

The experimental evidence that significantly contributed to the development of quantum mechanics is the Photoelectric effect. 

The photoelectric effect demonstrates that light can behave like particles (called photons) when it interacts with matter, causing electrons to be ejected from a metal surface. 

Explanation

In an intrinsic semiconductor, there are equal numbers of electrons in the conduction band and holes in the valence band

So the Fermi level, which represents the energy level at which the probability of finding an electron is 50%

Lies right in the middle of the band gap between the valence and conduction bands.