Fusion and stars

Physics · Nuclear and quantum physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

In fusion light nuclei join to make a heavier nucleus and release energy. Nuclei are positive and repel, so fusion needs a very high temperature, to make them move fast enough, and a high density, so that they collide often. Main-sequence stars fuse hydrogen into helium in the core.

A star is stable when the inward pull of gravity balances the outward pressure of radiation and hot gas.

The Hertzsprung–Russell diagram plots luminosity against surface temperature, with temperature increasing to the left. Most stars lie on the main sequence. Red giants are at the upper right and white dwarfs at the lower left. The mass of a star decides how it ends.

Rules to remember

Common mistake

Students read the temperature axis of the HR diagram the wrong way. Temperature increases to the left, so the hot stars are on the left and the cool red stars are on the right.

Worked example

A star is 400 times as luminous as the Sun and its surface temperature is twice that of the Sun. What is its radius in terms of the Sun's radius RS?

  1. L = 4πR²σT4, so R is proportional to √L ÷ T².
  2. √L factor: √400 = 20.
  3. T² factor: 2² = 4.
  4. R = (20 ÷ 4) RS = 5 RS.

Answer: 5 times the radius of the Sun

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