3C 273 was the first quasar to be discovered. IC 1101 is one of the largest galaxies known. Table 2 shows some information about these objects. Table 2 | Object | Absolute magnitude | Apparent magnitude | Distance / Mpc | |----------------|--------------------|--------------------|----------------| | quasar 3C 273 | X | 12.8 | 760 | | galaxy IC 1101 | -22.8 | 14.7 | 320 | State the property of the quasar that led to its discovery. Show that the absolute magnitude X of quasar 3C 273 is about -27. Assume that the quasar and the galaxy are both viewed from the same distance. Explain which would be the brighter object. Go on to calculate the ratio brightness of brighter object brightness of dimmer object. The black hole at the centre of IC 1101 has a mass of 7.1 × 10^11 M S where M S is the mass of the Sun. Calculate the average density within the event horizon of the black hole. ratio = ____________________________ average density = __________________ kg m -3

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3C 273 was the first quasar to be discovered - AQA - A-Level Physics - Question 3 - 2022 - Paper 4

Question 3

3C 273 was the first quasar to be discovered. IC 1101 is one of the largest galaxies known. Table 2 shows some information about these objects. Table 2 | Object ... show full transcript

Worked Solution & Example Answer:3C 273 was the first quasar to be discovered - AQA - A-Level Physics - Question 3 - 2022 - Paper 4

Step 1

State the property of the quasar that led to its discovery.

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Answer

The quasar 3C 273 is known for being a high power and powerful radio emitter, which was a significant property leading to its discovery.

Step 2

Show that the absolute magnitude X of quasar 3C 273 is about -27.

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Answer

To determine the absolute magnitude X, we use the formula that relates absolute and apparent magnitudes to distance: $M = m - 5 imes ( ext{log}_{10}(D) - 1)$ Where:

$M$ is the absolute magnitude
$m$ is the apparent magnitude (12.8 for 3C 273)
$D$ is the distance in parsecs (760 Mpc = 760 × 10^6 pc)

Now substituting the values: $M = 12.8 - 5 imes ( ext{log}_{10}(760 imes 10^6) - 1)$ Calculating gives:

Thus, $$M ext{ approximately equals } 12.8 - 5 imes (8.880 - 1) ext{ gives us } M ext{ around } -27.$$

Step 3

Explain which would be the brighter object.

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Answer

The quasar 3C 273 will be brighter than galaxy IC 1101 because it has a more negative absolute magnitude. In astronomy, a lower (or more negative) absolute magnitude indicates a brighter object. Given the absolute magnitudes of -27 for 3C 273 and -22.8 for IC 1101, quasar 3C 273 is indeed the brighter object.

Step 4

Go on to calculate the ratio brightness of brighter object brightness of dimmer object.

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Answer

The ratio of brightness can be calculated using the formula: $ext{Ratio} = 10^{(m_2 - m_1) / 5}$ Where:

$m_1$ is the apparent magnitude of the brighter object (3C 273), which is 12.8.
$m_2$ is the apparent magnitude of the dimmer object (IC 1101), which is 14.7.

Substituting the values: $ext{Ratio} = 10^{(14.7 - 12.8) / 5} = 10^{1.9 / 5} ext{ or approximately } 2.51$

Step 5

Calculate the average density within the event horizon of the black hole.

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Answer

To find the average density within the event horizon of the black hole, we need to use the formula:

ho = \frac{M}{V}$$ Where: - $ ho$ is the average density, - $M$ is the mass of the black hole ($7.1 imes 10^{11} M_S$), - $V$ is the volume of the black hole, calculated for a sphere: $$V = \frac{4}{3} \pi r^3$$ To find the radius $r$ use the Schwarzschild radius: $$r_s = \frac{2GM}{c^2}$$ Substitute $M = 7.1 imes 10^{11} M_S$ and use $M_S = 1.989 × 10^{30} kg$ for the sun's mass. Calculate volume and then density: $$ \rho = \frac{7.1 imes 10^{11} imes 1.989 × 10^{30} kg}{ \frac{4}{3} \pi (r_s)^3}$$ Calculating will yield the average density within the event horizon.

3C 273 was the first quasar to be discovered - AQA - A-Level Physics - Question 3 - 2022 - Paper 4

Worked Solution & Example Answer:3C 273 was the first quasar to be discovered - AQA - A-Level Physics - Question 3 - 2022 - Paper 4

State the property of the quasar that led to its discovery.

Show that the absolute magnitude X of quasar 3C 273 is about -27.

Explain which would be the brighter object.

Go on to calculate the ratio brightness of brighter object brightness of dimmer object.

Calculate the average density within the event horizon of the black hole.

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