Quantum Mechanics | MCQs

Explanation

The wavelength of the radiation emitted when an electron in a hydrogen atom jumps from a higher orbit (n = 2) to a lower orbit (n = 1) can be calculated using the Rydberg formula:

Explanation

 in every instant of time, the wavelength associated with a freely falling body decreases.

This is because the de Broglie wavelength 

λ of a particle is inversely proportional to its momentum:

(𝜆=ℎ/𝑝 ).

where:

• $h$ is Planck's constant,
• $p$ is the momentum of the particle.

Explanation

The momentum 

𝑝 of a photon is given by the equation:

𝑝=ℎ/𝜆 

where:

h is Planck's constant,

λ is the wavelength of the photon.

Since photons are massless, their momentum is not related to mass but to their wavelength.

Explanation

Einstein’s photoelectric equation is "hv = hvo + (1/2 mv^2) max", where:

• hv is the energy of the incident photon
• h is Planck's constant
• vo is the threshold frequency
• m is the mass of the emitted photoelectron
• max is the maximum kinetic energy of the emitted photoelectron.

Explanation

The dual character of matter particles in motion was postulated by De Broglie. 

Louis de Broglie proposed the idea that particles like electrons could behave not only as particles but also as waves, a concept known as wave-particle duality

Explanation

The Pfund series of hydrogen spectral lines occurs when electrons fall to the n = 5 energy level from higher levels.

These transitions emit radiation in the infrared (IR) region of the electromagnetic spectrum.

Explanation

The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers.

This principle helps to explain the arrangement of electrons in atoms.

Explanation

• High-speed electrons, such as those emitted in beta decay or used in electron microscopy, have wavelengths in the range of 10^-15 meters to 10^-12 meters.
• This is due to their high energy and momentum, which corresponds to a short wavelength according to the de Broglie hypothesis.

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

In quantum mechanics, the wave function $psi(x, t)$ describes the quantum state of a particle.

The probability density of finding the particle at a particular position in space is given by:

$$P(x) = |psi(x, t)|^2$$

This means:

• The square of the magnitude (or absolute value) of the wave function gives the probability per unit length (or volume) of finding the particle in that region.

• This principle is known as the Born interpretation.