Physics: Modern Physics

In special relativity, what happens to the time interval measured by a stationary observer for a clock moving at a significant fraction of the speed of light?

The time interval increases, a phenomenon known as time dilation, calculated as Δt = Δt₀ / sqrt(1 - v²/c²).

Explain why length contraction only occurs in the direction of motion according to special relativity.

Length contraction is a consequence of the Lorentz transformation where only the spatial dimension parallel to the velocity vector is scaled by the factor sqrt(1 - v²/c²).

What does the equation E = mc² represent regarding the relationship between mass and energy?

It states that mass and energy are equivalent and interchangeable; a small amount of mass can be converted into a large amount of energy.

In the photoelectric effect, why does increasing the intensity of light not increase the maximum kinetic energy of the emitted electrons?

Kinetic energy depends solely on the frequency of individual photons (E = hf - Φ); intensity only increases the number of photons and thus the number of electrons emitted.

How is the stopping potential (Vs) in a photoelectric experiment related to the maximum kinetic energy of the ejected photoelectrons?

The stopping potential is the voltage required to halt the most energetic electrons, defined by the equation eVs = Kmax = hf - Φ.

What is the relationship between a photon's momentum (p) and its wavelength (λ)?

Momentum is inversely proportional to wavelength, expressed by the formula p = h / λ, where h is Planck's constant.

State the de Broglie wavelength formula for a particle with mass (m) and velocity (v).

λ = h / (mv), where h is Planck's constant and mv is the momentum of the particle.

According to the Heisenberg Uncertainty Principle, what is the mathematical relationship between the uncertainty in position (Δx) and momentum (Δp)?

The product of the uncertainties must be greater than or equal to h-bar divided by two: Δx * Δp ≥ ħ / 2.

In the Bohr model of the hydrogen atom, what physical quantity is quantized to produce discrete energy levels?

The angular momentum (L) of the electron is quantized in integer multiples of h-bar (L = nħ).

What does the Pauli Exclusion Principle state regarding the quantum numbers of electrons in an atom?

No two electrons in the same atom can have the identical set of all four quantum numbers (n, l, ml, ms).