EM Radiation From Stars (OCR A Level Physics)

Algol is a triple-star system, with stars Aa1, Aa2 and Aa3 orbiting each other.

This triple-star is 90 light-years from the Earth.

Here is some data on the star Aa1. • radius = (1.90 ± 0.14) × 10⁹ m • mass = (6.31 ± 0.42) × 10³⁰ kg. Calculate the gravitational field strength g at the surface of Aa1 to 3 significant figures.

  Include the absolute uncertainty in your answer. Assume that the other stars of the system exert negligible gravitational force on Aa1.

g = .............................. ± .............................. N kg^–1 [4]

The table shows some data about the three stars of Algol.

Star Luminosity of star / L_Θ Surface temperature of star / K Aa1 182 13000 Aa2 6.92 4500 Aa3 10.0 7500

The luminosity of each star is in terms of the solar luminosity L_Θ.

i) Define the luminosity of a star.

[1]

ii) Use Stefan’s law to determine the ratio 

ratio = .......................................................... [2]

iii) Use Wien’s displacement law to explain which star would have the longest wavelength at the peak intensity of the emitted electromagnetic radiation.

[2]

iv) Suggest how an astronomer using just an optical telescope can deduce that the three stars of Algol have different surface temperatures.

[1]

v) The light from each star passing through a diffraction grating shows an absorption line spectrum.

Explain how a specific absorption line is produced in this type of spectrum in terms of photons and electrons.

[3]

The Aa1 star could evolve into a black hole. State two ways in which the black hole would differ from the Aa1 star. 1. ............................................................................................. 2. .............................................................................................

[2]

Fig. 21.1 shows some of the energy levels of electrons in hydrogen gas atoms. The energy levels are labelled A, B, C and D.

Fig. 21.1 (not to scale)

i) Explain why the energy levels are negative.

[1]

ii) An electron makes a transition (jump) from level C to level A.

1 Calculate the energy gained by this electron.

energy = ............................. eV [1]

2 Calculate the wavelength in nm of the photon absorbed by this electron.

wavelength = ............................. nm [3]

Light from a distant galaxy is passed through a diffraction grating. Fig. 21.2 shows the part of the spectrum of light that shows a strong hydrogen-alpha emission line.

Fig. 21.2

i) State how an emission line is produced.

[1]

ii) State an adjustment that could be made to the experimental arrangement that would space the emission lines more widely.

[1]

iii) In the laboratory, the wavelength of the hydrogen-alpha emission line is 656.3 nm.

Use Fig. 21.2 to determine the recession velocity of the galaxy.

recession velocity = .................................. m s⁻¹ [3]

iv) Suggest why hydrogen spectral lines play an important role in determining red shift of galaxies.

[1]

Light from a similar star is viewed in a galaxy further away. The star is part of a pair of stars which orbit a common centre of mass. Describe and explain how the equivalent spectrum might appear.

[3]

A group of students are conducting an experiment to determine the wavelength of monochromatic light from a laser.

Fig. 24.1 shows the laser beam incident normally at a diffraction grating.

Fig. 24.1

The students use a diffraction grating with 600 lines mm⁻¹.

They vary the distance between the grating and the screen from 1.000 m to 2.000 m. They measure the distance  from the central maximum to the second order maximum.

The students decide to plot a graph of against .

Show that the gradient of the graph is equal to sin θ, where θ is the angle between the central maximum and the second order maximum.

[1]

Fig. 24.2 shows the graph plotted by the students.

Fig. 24.2

i) Use Fig. 24.2 to determine an accurate value of the wavelength λ of the light from the laser.

λ = ..................................................... m [3]

ii) Suggest why there are no error bars shown in Fig. 24.2.

 [1]

iii) Suggest how the precision of this experiment may be affected by using a protractor to measure the angle θ.

 [1]