9 Introduction to Modern Physics Free Online FlashCards

What two principles underlie special relativity?

Special relativity applies to inertial frames, where the laws of physics are the same and every observer measures the same vacuum speed of light, $c$.

How does an observer measure the interval on a moving clock?

A moving clock’s interval is measured as longer: $\Delta t=\gamma\Delta\tau$, where $\Delta\tau$ is the proper time and $\gamma=1/\sqrt{1-v^2/c^2}$.

How does motion affect an object's length along its direction of travel?

Along the direction of motion, the observed length is contracted: $L=L_0/\gamma$, where $L_0$ is the object’s rest length.

Why can brighter light fail to eject electrons in the photoelectric effect?

Increasing light intensity increases the number of photons, not each photon’s energy. In the photoelectric effect, electron ejection requires photon energy high enough to overcome the material’s work function.

What is the de Broglie wavelength of a particle with momentum $p$?

A particle with momentum $p$ has de Broglie wavelength $\lambda=h/p$.

What does $|\Psi|^2$ represent in quantum mechanics?

The wave function $\Psi$ describes the quantum state; $|\Psi|^2$ gives the probability density for a position measurement, not a precise classical path.

What limit does the position–momentum uncertainty principle express?

The uncertainty principle sets a fundamental limit: $\Delta x\,\Delta p\geq\hbar/2$. It is not merely a consequence of imperfect instruments.

What distinguishes isotopes of the same element?

The atomic number $Z$, equal to the number of protons, identifies an element. Isotopes of that element have different numbers of neutrons.

What is the energy of hydrogen’s level with principal quantum number $n$?

In the simplest hydrogen model, the energy levels are $E_n=-13.6\,\text{eV}/n^2$, where $n=1,2,3,\ldots$.

What determines the energy of a photon emitted in an atomic transition?

An electron absorbs or emits a photon when it changes energy state; the photon energy equals the magnitude of the energy difference: $hf=|\Delta E|$.

How is a nucleus’s mass defect related to its binding energy?

A nucleus has less mass than its separated nucleons. This mass defect corresponds to binding energy: $E_b=\Delta m c^2$.

What is a radioactive sample’s half-life?

The half-life is the time for half the nuclei in a large sample to decay: $T_{1/2}=\ln 2/\lambda$. Individual decays are unpredictable, but large populations are statistically predictable.