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Fusion and Stars · Paper 2 — Free Physics HL Practice Questions

1MasterySAQ-SLife cycle of stars6 marksPaper 2~9 min

A main sequence star has a mass of

2.0 \times 10^{30}\,\text{kg}

and a luminosity of

3.8 \times 10^{26}\,\text{W}

. During the main sequence phase, hydrogen is fused into helium at a rate of

6.0 \times 10^{11}\,\text{kg s}^{-1}

. Speed of light:

c = 3.0 \times 10^{8}\,\text{m s}^{-1}

(a)

State the two opposing forces that maintain hydrostatic equilibrium during the main sequence phase of a star. [1 mark]

(b)

Calculate the fraction of the mass consumed per second that is converted into energy. [3 marks]

(c)

Only approximately 10 percent of the star's total mass is available as hydrogen fuel in the core. Deduce the main sequence lifetime of this star in years. [2 marks]

Solutions

2MasterySAQ-SLife cycle of stars7 marksPaper 2~11 min

A red giant star has the following properties: Quantity — Value Radius —

5.0 \times 10^{10}\,\text{m}

Luminosity —

1.0 \times 10^{28}\,\text{W}

Stefan–Boltzmann constant

\sigma

—

5.67 \times 10^{-8}\,\text{W\,m}^{-2}\,\text{K}^{-4}

(a)

State what happens to the core of a main-sequence star when its hydrogen fuel is exhausted. [1 mark]

(b)

Calculate the surface temperature of this red giant. [3 marks]

(c)

The peak wavelength of radiation emitted by the Sun is

5.0 \times 10^{-7}\,\text{m}

. Using your answer to (b) and Wien's displacement law (

\lambda_{\max} T = 2.90 \times 10^{-3}\,\text{m\,K}

), deduce whether this red giant emits peak radiation at a longer or shorter wavelength than the Sun, and calculate the ratio

\dfrac{\lambda_{\max,\,\text{giant}}}{\lambda_{\max,\,\odot}}

. [3 marks]

Solutions

3MasterySAQ-SLife cycle of stars5 marksPaper 2~8 min

A star has an initial mass of

8.0 \times 10^{30}\,\text{kg}

. It converts hydrogen to helium;

0.71\%

of the mass consumed is released as energy. The star's luminosity (power output) is

3.8 \times 10^{26}\,\text{W}

. Only

10\%

of the star's mass is available for fusion in the core.

(a)

State the condition that determines when a star leaves the main sequence. [1 mark]

(b)

Calculate the rate at which the star must consume hydrogen mass to sustain its luminosity of

3.8 \times 10^{26}\,\text{W}

. [2 marks]

(c)

Calculate the time, in years, that the star spends on the main sequence. [2 marks]

Solutions

4ChallengeSAQ-LNuclear fusion and energy production in stars8 marksPaper 2~12 min

Data

- Mass of one proton:

m_p = 1.6726 \times 10^{-27}\,\text{kg}

- Mass of a helium-

4

nucleus:

m_{\text{He}} = 6.6447 \times 10^{-27}\,\text{kg}

- Mass of one positron:

m_{e^+} = 9.109 \times 10^{-31}\,\text{kg}

- Mass of one electron neutrino:

\approx 0\,\text{kg}

- Speed of light:

c = 3.00 \times 10^{8}\,\text{m\,s}^{-1}

- Sun's total power output:

L_\odot = 3.85 \times 10^{26}\,\text{W}

The proton–proton chain the core of a star like the Sun converts four protons into a helium-

4

nucleus. The overall reaction is:

4\,^1_1\text{H} \rightarrow\, ^4_2\text{He} + 2e^+ + 2\nu_e + \gamma

(a)

Calculate the mass defect

\Delta m

for a single fusion event in which four protons fuse to produce one helium-

4

nucleus and two positrons. [2 marks]

(b)

Calculate the energy released per fusion event in joules. [1 mark]

(c)

Calculate the number of fusion events occurring in the Sun per second. [2 marks]

(d)

Explain why the positrons produced in the reaction do not represent a long-term mass loss from the star. [2] (e) The neutrinos produced in the proton–proton chain carry away approximately

2\,\text{percent}

of the energy released per fusion event. Evaluate the significance of neutrino emission for the energy balance of the Sun, referring to both the immediate energy budget and the long-term stability of the star. [3 marks]

Solutions

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