Modern Physics Test. 5

The spacetime interval, defined as (Δs)² = (cΔt)² - (Δx)², is an invariant quantity in special relativity, meaning all inertial observers will calculate the same value for it.

Momentum, total energy (mass-energy), and charge are all fundamental quantities that are conserved in this process.

Using Einstein's equation E = mc². Energy = 2 kg * (3 x 10⁸ m/s)² = 2 * (9 x 10¹⁶) = 1.8 x 10¹⁷ Joules.

Einstein's 1905 paper explained the features of the photoelectric effect by postulating that light itself is made of discrete energy quanta, which he called photons.

Visible light photons have energies of a few electron-volts, which is far below the minimum energy threshold of 1.02 MeV required to create an electron-positron pair.

The classical Rayleigh-Jeans law predicted infinite energy emission at short wavelengths, a failure famously dubbed the 'Ultraviolet Catastrophe'.

The maximum kinetic energy is directly related to the stopping potential by K.E.max = e*Vs. A stopping potential of 1.5 Volts corresponds to a kinetic energy of 1.5 electron-Volts.

From ΔE Δt ≥ ħ/2, if ΔE = 0, then Δt must be infinitely large. This means a state with a perfectly defined energy must be stable and exist forever.

Einstein's explanation of the photoelectric effect solidified the idea that light, long considered a wave, also has particle-like properties (photons).

This is a key consequence of special relativity. Whether two spatially separated events occur at the same time depends on the observer's state of motion.

The uncertainty principle dictates an inverse relationship. A small uncertainty in position (Δx) necessarily leads to a large uncertainty in momentum (Δp).

The total energy is the sum of the energy a particle has due to its mass (m₀c²) and the additional energy it has due to its motion (K.E.).

The relationship is given by Planck's fundamental equation, E = hf.

This is the definition of quantization. The quantity is restricted to specific, discrete levels rather than being able to take on any continuous value.

Relativistic momentum is p = γm₀v. At 0.99c, the Lorentz factor γ is approximately 7.1, so the momentum is over 7 times its classical value.

The experiment's 'null result' famously failed to detect the hypothetical ether wind, which was a crucial step towards the development of special relativity.

Half-life T = 0.693 / lambda. So, T = 0.693 / 0.0231 per day = 30 days.

Diffraction effects are prominent only when the wavelength of a wave is similar in size to the aperture or spacing of a grating, which in this case was the crystal lattice.

According to Wien's displacement law, doubling the temperature shifts the peak emission to a much shorter wavelength, into the blue or ultraviolet part of the spectrum.

From the energy-momentum relation E² = (pc)² + (m₀c²)², if rest mass m₀=0, then E=pc. This relationship only holds for particles, like photons, that travel at speed c.