Physica — Interactive Physics Formula Explorer

Nuclear & Particle★★★★★

E = mc^2

Mass is a highly concentrated form of energy; converting even a tiny mass releases enormous energy.

Nuclear & Particle★★★★★

N(t) = N_0 e^{-\lambda t}

Undecayed nuclei fall exponentially; each has a fixed decay probability per unit time.

Nuclear & Particle★★★★★

T_{1/2} = \frac{\ln 2}{\lambda}

Half-life is a fixed isotope property—independent of the sample size.

Nuclear & Particle★★★★★

B = \Delta m \, c^2

The missing mass when nucleons bind into a nucleus appears as the energy holding them together.

Nuclear & Particle★★★★★

Q = (m_i - m_f) c^2

Lighter products mean the missing mass exits as kinetic energy and radiation.

Nuclear & Particle★★★★★

E^2 = (pc)^2 + (mc^2)^2

Energy and momentum combine to form a Lorentz invariant — the rest mass of the particle.

Nuclear & Particle★★★★★

\lambda = \frac{h}{p}

A particle’s wavelength shrinks with momentum—more momentum probes smaller scales.

Nuclear & Particle★★★★★

\log_{10} T_{1/2} = a \frac{Z}{\sqrt{Q}} + b

Alpha half-lives vary exponentially with decay energy via quantum tunneling.

Nuclear & Particle★★★★★

B(A,Z) = a_V A - a_S A^{2/3} - a_C \frac{Z^2}{A^{1/3}} - a_A \frac{(A-2Z)^2}{A} + \delta(A,Z)

Five competing terms—volume, surface, Coulomb, asymmetry, pairing—model the nuclear binding energy.

Nuclear & Particle★★★★★

\frac{d\sigma}{d\Omega} = \frac{1}{2} \alpha^2 r_c^2 \left(\frac{\omega'}{\omega}\right)^2 \left[\frac{\omega}{\omega'} + \frac{\omega'}{\omega} - \sin^2\theta\right]

QED correction to Thomson scattering: photon cross-section shrinks at high energy.