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).

$^{235}\text{U} + \text{n} \to ^{141}\text{Ba} + ^{92}\text{Kr} + 3\text{n}$. 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.

State Einstein's mass-energy equivalence. [2 marks]

A mass defect of $0.030 \text{ u}$ accompanies a fusion reaction. Calculate the energy released in MeV. [3 marks]

A $^{235}\text{U}$ fission has $\Delta m = 0.215 \text{ u}$. (a) Calculate the energy released in J and MeV. (b) Calculate the energy per kilogram of $^{235}\text{U}$ ($m_{nucleus} = 235.04 \text{ u}$).