Fusion and stars practice questions.

A main-sequence star remains in stable equilibrium for billions of years. Which pair of effects balance to produce this stability?

• Inward gravitational pressure and outward radiation (and gas) pressure
• Inward radiation pressure and outward gravitational pressure
• Electrostatic repulsion between nuclei and the strong nuclear force
• Magnetic pressure and centripetal force due to the star's rotation

Answer: Inward gravitational pressure and outward radiation (and gas) pressure

Gravity pulls the stellar material inward, while the radiation and gas pressure generated by core fusion pushes outward; on the main sequence these are in equilibrium.

Explain why extremely high temperatures are required for nuclear fusion to occur in a stellar core.

• High temperatures split the nuclei into free quarks that can recombine
• The strong nuclear force only acts at high temperatures
• High temperatures completely ionize the gas so that the electrons no longer shield the positive nuclei
• The nuclei need enough kinetic energy to overcome their mutual electrostatic repulsion

Answer: The nuclei need enough kinetic energy to overcome their mutual electrostatic repulsion

Both nuclei are positively charged; only at very high temperatures do they have sufficient kinetic energy to approach within range of the attractive strong nuclear force.

The black-body spectrum of star A peaks at 400 nm and that of star B peaks at 800 nm. Determine the ratio of their surface temperatures T_A : T_B.

• 1 : 2
• 2 : 1
• 4 : 1
• 16 : 1

Answer: 2 : 1

By Wien's law λmax × T = constant, so T is inversely proportional to λmax: T_A/T_B = 800/400 = 2, giving 2 : 1.

The surface temperature of a star doubles while its radius stays constant. By what factor does its luminosity change?

• × 2
• × 4
• × 8
• × 16

Answer: × 16

From the Stefan-Boltzmann law L = σAT⁴, luminosity scales with T⁴, so doubling T multiplies L by 2⁴ = 16.

The distance between an observer and a star of constant luminosity is doubled. What happens to the apparent brightness measured by the observer?

• It halves
• It falls to one quarter of its original value
• It stays the same, because luminosity is unchanged
• It falls to one eighth of its original value

Answer: It falls to one quarter of its original value

Apparent brightness b = L / (4πd²) follows an inverse-square law, so doubling d reduces b by a factor of 2² = 4.

On a Hertzsprung-Russell diagram, where are white dwarfs located and why?

• Top right, because they are cool and very luminous
• Top left, because they are hot and very luminous
• Bottom left, because they are hot but have low luminosity due to their small surface area
• Bottom right, because they are relatively cool stars and therefore have a very low luminosity

Answer: Bottom left, because they are hot but have low luminosity due to their small surface area

White dwarfs have high surface temperatures but very small radii; by L = σAT⁴ their tiny surface area keeps the luminosity low, placing them in the lower left of the HR diagram.