# CIE AS & A Level Physics : 25.1 Standard candles – Exam style question – Paper 4

### Question

(a)    State what is meant by luminosity of a star.

(b)    The luminosity of the Sun is $$3.83 \times 10^{26}$$ W. The distance between the Earth and the Sun is $$1.51 \times 10^{11} m$$.

Calculate the radiant flux intensity F of the Sun at the Earth. Give a unit with your answer.

(c)     Use data from (b) to calculate the mass that is converted into energy every second in the Sun.

(d)    The radius of the Sun is $$6.96 \times 10^{8}$$ m.

Show that the temperature T of the surface of the Sun is $$5770$$ K.

(e)    The wavelength $$λ_{max}$$ of light for which the maximum rate of emission occurs from the Sun is $$5.00 \times 10^{–7}$$m.

The temperature of the surface of the star Sirius is $$9940$$ K.

Use information from (d) to determine the wavelength of light for which the maximum rate of emission occurs from Sirius.

Ans:

(a)     total power of radiation emitted (by the star)

(b)     $$F$$ = $$\frac{L}{4\pi d^{2}}$$

= $$\frac{3.83\times 10^{26}}{4\times \pi 1.51\times 10^{112}}$$

= $$1340 W\, m^{-2}$$

(c)     $$m = \frac{E}{c^{2}}$$

= $$\frac{3.83\times 10^{26}}{3.00\times 10^{82}}$$

= $$4.26 \times 10^{9}$$ kg

(d)    $$L = 4\pi \sigma r^{2}T^{4}$$

$$3.83 \times 10^{26}$$ = $$4\times \pi 5.67\times 10^{-8}\times 6.96 \times 10^{82}\times T^{4} leading to T$$ = $$5770$$ K

(e)      $$\lambda _{(max)} \frac{1}{T}$$

$$\frac{5.00 \times 10^{-7}}{\lambda} = \frac{9940}{5770}$$

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