Quick questions on Mass-energy equivalence $E = mc^2$ (QCE Physics Unit 4)

These values are used throughout particle and nuclear physics. The proton and neutron rest energies are nearly equal but the neutron is slightly heavier (its instability to beta decay is consistent with this).

As $v \to c$, $\gamma \to \infty$ and $E \to \infty$. Infinite energy would be required to accelerate a particle with rest mass to the speed of light; no such particle ever reaches $c$.

$1$ amu $= 1.661 \times 10^{-27}$ kg. The rest energy of 1 amu is:

$^{235}\text{U} + \text{n} \to ^{141}\text{Ba} + ^{92}\text{Kr} + 3\text{n}$. Mass deficit approximately 0.2 atomic mass units (amu). Energy released approximately 200 MeV per fission event.

$^2\text{H} + ^3\text{H} \to ^4\text{He} + \text{n}$. Mass deficit approximately 0.0188 amu. Energy released approximately 17.6 MeV per fusion event.

A high-energy photon (energy at least $2 m_e c^2 = 1.022$ MeV) can convert into an electron-positron pair in the presence of a nucleus (which carries away momentum to conserve momentum). Total mass appears from total energy.

An electron and a positron annihilate to two photons (back-to-back, each with energy $0.511$ MeV in the centre-of-mass frame). All rest mass is converted to electromagnetic energy. This is the basis of PET (positron emission tomography) medical imaging.

The sun converts about $4 \times 10^9$ kg of mass to energy per second through hydrogen fusion. Total solar luminosity: $4 \times 10^{26}$ W. The sun has about $2 \times 10^{30}$ kg of mass and will continue fusing hydrogen for another 5 billion years.

Stellar core collapse converts substantial mass to energy, producing the most luminous events in the universe. Type Ia supernovae are used as "standard candles" because their peak luminosity is calibrated.

Matter falling into a black hole can convert up to about 40 percent of its rest energy to radiation, the most efficient natural energy source known.

$E_0 = m c^2$ is the rest energy. $E = \gamma m c^2$ is the total relativistic energy.

Mass in kg requires $c^2$ in (m/s)$^2$ to give energy in joules. Convert to MeV using $1$ eV $= 1.6 \times 10^{-19}$ J or $1$ amu $\equiv 931.5$ MeV.

$E = mc^2$ is the rest energy. The total energy of a moving particle is $\gamma m c^2$, larger by a factor of $\gamma$.

In relativity, mass and energy are different forms of the same quantity. Mass is "frozen energy"; energy is "active mass". The conversion factor is $c^2$.

Photons have rest mass zero but carry energy and momentum. Use $E = pc$ for photons.