Modern Physics Test. 6

In the modern quantum interpretation, the square of the amplitude of the matter wave at a point is proportional to the probability of finding the particle at that point.

The work function is an intrinsic, characteristic property of a specific material, representing how tightly its electrons are bound to the surface.

The situation is not symmetrical. The traveling twin must accelerate to leave, turn around, and return. This acceleration places them in non-inertial frames, breaking the symmetry and causing a real age difference.

This 'backscattering' angle of 180° corresponds to the maximum energy transfer to the electron and thus the maximum increase in the photon's wavelength.

The photon transfers some of its energy to the electron, so its final energy (E') must be less than its initial energy (E), unless the scattering angle is zero.

This formula shows that the measured (relativistic) mass 'm' of an object increases with its velocity relative to the observer, from its rest mass 'm₀'.

An activity of 25% (or 1/4th) means two half-lives have passed (100% -> 50% -> 25%). The age is 2 * 5730 years = 11460 years.

The radius R = R₀ * (A to the power of 1/3). R = (1.2 x 10⁻¹⁵ m) * 4.12 = 4.944 x 10⁻¹⁵ m.

Confining the particle to a smaller space decreases the uncertainty in its position (Δx). By the Heisenberg Uncertainty Principle, this must cause an increase in the uncertainty of its momentum (Δp).

A black body emits radiation at all wavelengths, forming a continuous spectrum whose shape and peak intensity depend only on the body's temperature.

Using E = m₀c², the electron's rest mass energy is calculated to be approximately 0.511 Mega-electron-volts (MeV), a fundamental constant in particle physics.

The total energy produced is the sum of the rest mass energies of both particles. Total Energy = 0.511 MeV + 0.511 MeV = 1.022 MeV.

Helium-4 has 4 nucleons (2 protons, 2 neutrons). Binding energy per nucleon = Total binding energy / number of nucleons = 28.3 MeV / 4 = 7.075 MeV.

The resolution of any imaging system is fundamentally limited by diffraction. To 'see' an object's features, the wavelength used must be smaller than those features.

A photocell is a direct application where incident light ejects electrons from a surface, creating a measurable electric current, which is the definition of the photoelectric effect.

The activity reduced from 8000 -> 4000 -> 2000 -> 1000. This is a reduction by a factor of 8 (2*2*2), which means 3 half-lives have passed in 6 hours. So, the half-life is 6 hours / 3 = 2 hours.

The late 19th and early 20th centuries saw the emergence of problems (like blackbody radiation) that classical physics could not solve, heralding the new era of modern physics.

The Davisson-Germer experiment showed that a beam of electrons could be diffracted by a crystal lattice, a behavior that is exclusively characteristic of waves.

Number of half-lives = 500 / 100 = 5. Atoms remaining = (6.4 x 10²⁰) * (1/32) = 0.2 x 10²⁰. Atoms decayed = Initial - Remaining = (6.4 x 10²⁰) - (0.2 x 10²⁰) = 6.2 x 10²⁰ atoms.