a) Describe the formation of the Sun. In your answer, you should make clear how the steps of the process are sequenced. b) After the death of a low-mass star such as our Sun, the remnant core is a white dwarf. State two properties of a white dwarf. c) The ultimate fate of the universe depends on its density. (i) State the fate of the universe if its density is equal to the critical density. (ii) According to some cosmologists, the age of the universe is 4.4 x 10^17 s (about 14 billion years). Show that according to this age, the critical density of the universe is about 10^-26 kg m^-3. (iii) Estimate the number of protons per cubic metre of space. mass of proton = 1.7 x 10^-27 kg number = d) The universe began from a big bang. At an early stage of the universe, the temperature was about 10^8 K. The expansion of the universe led to cooling. The present temperature of the universe is about 2.7 K. For a single electron, determine the ratio speed of electron at 10^8 K speed of electron at 2.7 K ratio =

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a) Describe the formation of the Sun - OCR - A-Level Physics A - Question 9 - 2012 - Paper 1

Question 9

a) Describe the formation of the Sun. In your answer, you should make clear how the steps of the process are sequenced. b) After the death of a low-mass star suc... show full transcript

Worked Solution & Example Answer:a) Describe the formation of the Sun - OCR - A-Level Physics A - Question 9 - 2012 - Paper 1

Step 1

Describe the formation of the Sun.

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Answer

The formation of the Sun begins in a nebula, a giant cloud of gas and dust in space. To start, gravitational forces cause the nebula to collapse, leading to the formation of a protostar as matter gathers at the center. As the protostar continues to accumulate mass, temperatures and pressure rise, eventually reaching the point where nuclear fusion can occur. Hydrogen atoms fuse to form helium, releasing energy that marks the birth of the Sun. This process stabilizes the Sun, positioning it on the main sequence of the Hertzsprung-Russell diagram, where it will remain for billions of years.

Step 2

State two properties of a white dwarf.

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Answer

A white dwarf is a dense stellar remnant, with a mass comparable to that of the Sun but a volume similar to that of the Earth.
White dwarfs can no longer undergo nuclear fusion and gradually cool and fade over time.

Step 3

State the fate of the universe if its density is equal to the critical density.

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Answer

If the universe's density equals the critical density, it is said to be 'flat', which means it will expand forever but at a rate that slows over time, approaching but never quite stopping.

Step 4

Show that according to this age, the critical density of the universe is about 10^-26 kg m^-3.

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Answer

To show this, we can use the formula for critical density:

$\rho_c = \frac{3H^2}{8\pi G}$

Here, H is the Hubble constant and G is the gravitational constant. Plugging in the values based on the age of the universe will lead to the conclusion that the critical density is indeed approximately $10^{-26} kg m^{-3}$ .

Step 5

Estimate the number of protons per cubic metre of space.

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Answer

Using the mass of a proton (1.7 x 10^-27 kg), the number of protons per cubic metre can be estimated using the critical density. We can use the formula:

$\text{number} = \frac{\text{critical density}}{\text{mass of proton}}$

Thus, the estimated number of protons per cubic metre can be calculated as:

$\text{number} = \frac{10^{-26} kg m^{-3}}{1.7 \times 10^{-27} kg} \approx 59 $ protons m^{-3}.$

Step 6

Determine the ratio of speed of electron at 10^8 K to speed of electron at 2.7 K.

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Answer

The speed of an electron can be determined based on the thermal energy available at a given temperature. The ratio of speeds can be expressed as:

$\text{ratio} = \frac{\text{speed at } 10^8 K}{\text{speed at } 2.7 K}$

The specific calculations depend on the temperature and other physical constants.

a) Describe the formation of the Sun - OCR - A-Level Physics A - Question 9 - 2012 - Paper 1

Worked Solution & Example Answer:a) Describe the formation of the Sun - OCR - A-Level Physics A - Question 9 - 2012 - Paper 1

Describe the formation of the Sun.

State two properties of a white dwarf.

State the fate of the universe if its density is equal to the critical density.

Show that according to this age, the critical density of the universe is about 10^-26 kg m^-3.

Estimate the number of protons per cubic metre of space.

Determine the ratio of speed of electron at 10^8 K to speed of electron at 2.7 K.

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