Question 2 
To gain full marks you must clearly show your working in any calculation and express your answers to an appropriate number of significant figures. 

(a) A proton of mass mp = 1.673 × 10−27 kg and electric charge e = 1.602 × 10–19 C, and an electron of mass me = 9.109 × 10–31 kg and electric charge −e = −1.602 × 10–19 C, are not moving and are at a distance 1.000 × 10–10 m apart. 

You may assume that the electric constant, ke, is 8.988 × 109 N m2 C–2 and the gravitational constant, G, is 6.672 × 10–11 N m2 kg–2 . 

(i) Calculate the magnitude (numeric value) of the electric force between the proton and electron. Express your answer in scientific notation. State whether this force is attractive or repulsive. 
(ii) Calculate the magnitude of the gravitational force between the proton and electron. Express your answer in scientific notation. State whether this force is attractive or repulsive. 

(b) If the electron was replaced by another proton 
(i) state whether the magnitude of each of the electric and gravitational forces would increase, decrease or remain the same as in 2(a) 
(ii) state whether the direction of each of the electric and gravitational forces would reverse or remain the same as in 2(a). 

(c) Under conditions of high temperature, two protons could combine to form a deuterium nucleus in the following reaction: 

p + p -------  2H + e+ + ve + energy 
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where 2H  is a deuterium nucleus, e+ is a positron (i.e. the antimatter counterpart of an electron) and ve is an electron neutrino. 
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(i) State which of the four fundamental interactions are involved in this reaction and explain their roles. 
(ii) Write down an equation for this reaction in terms of the nucleons involved by replacing the deuterium nucleus with the appropriate protons and neutrons. 
(iii) Write down an equation for this reaction in terms of the quarks involved by replacing the protons and neutrons with the appropriate up and down quarks. 
(iv) Draw a Feynman diagram to represent the reaction at the quark level by indicating how one of the quarks changes flavour and gives rise to the emission of the positron and the electron neutrino. (You may produce your diagram using a computer if you wish. )

Question 3 

(a) (i) In no more than three sentences, state the Hubble relationship in words, and quantify numerically what it says about the speed of recession of distant galaxies. Include in your answer a definition of the unit one parsec. 
(ii) In a further two or three sentences, explain what the Hubble relationship tells us about the Universe and what it implies about the density of the Universe in the distant past. 

(b) Spectral lines from hydrogen are detected in the light from a distant galaxy. The blue line (rest wavelength, λ0 = 410.2 nm) is observed with a wavelength of 430.7 nm. 
(i) In no more than three sentences, explain whether the galaxy exhibits a red-shift or a blue-shift, and explain whether the galaxy is receding from or approaching the Earth. 
(ii) Calculate the numerical value of the red-shift or blue-shift exhibited by the galaxy. 
(iii) Calculate the speed, in km s–1, at which the galaxy is moving with respect to Earth, and express your answer in scientific notation. (You may assume that the speed of light is 3.00 × 105 km s–1) 
(iv) Assuming that the Hubble constant has a value of 60.0 km s−1 Mpc−1 , calculate the distance to the galaxy in Mpc. 

In order to gain full marks on part (b) you must show all your working and express your answers to an appropriate number of significant figures, using scientific notation where appropriate. 

Question 4 

(a) Define what is meant by a black-body. Sketch black-body spectra for two objects: one at temperature T1 and the other T2 where T1 > T2. 

(b) A black-body spectrum is found to have a corresponding mean photon energy of 1.55 eV. What is the temperature of the object that gives rise to this black-body spectrum? 

(c) Explain how the concept of black-body radiation has been used to interpret the cosmic microwave background, and hence how this provides evidence for the ‘Big Bang’ (no more than 200 words). 

(d) Briefly explain what is meant by the ‘open’ and ‘closed’ models of the future universe (no more than 200 words).