Modern Physics Test. 3

This is a consequence of time dilation and the principle of relativity. From the spaceship's frame of reference, Earth is the moving clock, and it is therefore observed to be running slower.

The law (P = σAT⁴) states that the total power radiated is directly proportional to the fourth power of the absolute temperature.

Max Planck introduced this fundamental constant of nature (h ≈ 6.626 x 10⁻³⁴ J·s) to explain the quantization of energy in blackbody radiation.

GPS requires corrections from both: special relativity for the high speed of the satellites (time dilation) and general relativity for the weaker gravitational field they experience.

Max Planck's successful solution to the blackbody radiation problem required the revolutionary assumption that the energy of oscillators was quantized.

This relation (often written with ħ = h/2π) indicates that a state that exists for a short time (small Δt) has a large uncertainty in its energy (large ΔE).

This is the second postulate of special relativity: the speed of light in a vacuum, 'c', is constant for all inertial observers, regardless of the source's or observer's motion.

Higher intensity means more photons arriving per second. If the frequency is above the threshold, this results in more electrons being ejected per second, leading to a larger current.

The relativistic factor gamma (γ) only becomes significantly greater than 1, causing a noticeable mass increase, as velocity approaches the speed of light, c.

Let K₁ = hf - φ. The new energy is K₂ = h(2f) - φ = 2hf - φ. Substituting hf = K₁ + φ gives K₂ = 2(K₁ + φ) - φ = 2K₁ + φ. Since φ > 0, K₂ > 2K₁.

The regular atomic spacing in the nickel crystal acted as a natural diffraction grating for the electron waves, producing the observed interference pattern.

From the equation E=hf, we can see that h=E/f. The units are Joules / (1/second), which is Joule-seconds (J·s), a unit of angular momentum or action.

Intensity is total energy per second. Since blue light photons have more energy individually than red light photons, more of the lower-energy red photons are needed to deliver the same total energy per second.

Mass is converted into energy according to E=mc², typically producing high-energy photons (gamma rays).

The wave model predicted a time delay for energy to accumulate. The instantaneous emission supports the particle model, where a single photon's energy is transferred to an electron in a single, immediate event.

In the realm of everyday experience (slow speeds, large objects), the effects of relativity and quantum mechanics are negligible, and classical physics provides extremely accurate predictions.

Using the formula f = E/h, we get (3.3 × 10⁻¹⁹ J) / (6.6 × 10⁻³⁴ J·s) = 0.5 × 10¹⁵ Hz, which is also 5.0 x 10¹⁴ Hz.

Since wavelength is inversely proportional to momentum (λ = h/p), doubling the momentum will halve the wavelength.

The principle is a fundamental property of nature. The wavelike nature of a particle means its position and momentum are inherently 'fuzzy' and cannot be simultaneously defined with perfect precision.

Phenomena like blackbody radiation, the photoelectric effect, and atomic spectra directly contradicted the predictions of classical theories, necessitating the new approaches of relativity and quantum mechanics.