Earth 1

Einstein, Planck and the Sun

Light & Mass

Mass is energy at rest. Light is energy in motion with no mass at all.

Mass is frozen energy

Energy, in joules. The energy locked inside a mass sitting still (its rest energy).
Rest mass, in kilograms. The mass you would measure on a scale.
The speed of light squared: (3 × 10⁸ m/s)² = 9 × 10¹⁶. This huge number is why a little mass holds a lot of energy.
Mass
1.00 × 10⁻³ kg
Energy
8.99 × 10¹³ J
In electron-volts
5.61 × 10³² eV
TNT equivalent
2.15e+4 tonnes

Fully converting 1 gram would release about 9 × 10¹³ J, roughly the Hiroshima bomb (≈ 15 kilotons). The bomb itself converted under one gram.

Light has energy and momentum but no mass

Planck’s constant, 6.626 × 10⁻³⁴ J·s: the size of one quantum of action.
Frequency: how many wave crests pass per second (Hz).
Wavelength: crest-to-crest distance. Shorter λ means more energy per photon.
Momentum. Light pushes: solar sails ride on this.
Frequency f
5.45 × 10¹⁴ Hz
Photon energy
2.254 eV
Momentum p
1.20 × 10⁻²⁷ kg·m/s
Rest mass
0 (exactly)

A photon carries energy E/c² = 4.02 × 10⁻³⁶ kg-equivalent, but its rest mass is zero. That’s why it can only ever move at c.

The full equation: Pythagoras for energy

Total energy is the hypotenuse of a right triangle. One side is momentum energy pc, the other is rest energy mc². At rest p = 0, so E = mc². For light m = 0, so E = pc. Slide the rest mass to zero and watch the triangle flatten into a photon.

Mass defect: where the Sun’s energy comes from

Protons (counted with their electrons as hydrogen atoms, m_H = 1.007825 u).
Neutrons, each m_n = 1.008665 u.
The measured mass of the whole atom. It is always a little less than its parts.
Binding energy: the energy released when the nucleus formed. 1 u of mass is 931.5 MeV.
Parts
2 p + 2 n
Mass defect Δm
0.03038 u (0.76%)
Binding energy
28.3 MeV
Per nucleon
7.074 MeV
H-21.11
He-47.07
C-127.68
O-167.98
Fe-568.79
U-2357.59
U-2387.57

Iron-56 is near the top: its nucleons are the most tightly bound. Fusing light nuclei up toward iron releases energy, which is how the Sun turns about 4 million tonnes of mass into light every second. Splitting heavy uranium down toward iron also releases energy: fission.