Hello,

I am running late on this one and wondering if someone would help me out? I've already started working on those, but it might be quicker if I start in the right direction. Thank you so much for your help.

Question 4 a. In Topic 10 (Part 4, Activity 4.1), you were asked to plot a graph of peak wavelength (on the vertical axis) against mean surface temperature (on the horizontal axis) for the position of the peak in the continuous black-body emission spectrum, based on the spectra emitted by seven different star types: 0, B, A, F, G, K and M. Your graph should include a best-fit curve plotted through the data points, and could be hand-drawn or computer-generated. i. Provide an appropriately titled and labelled table of the data you obtained in Activity 4.1, that is, the data you used to plot your graph. ii. Copy and paste your graph from Activity 4.1 into your TMA answer. Ensure you show the best-fit curve for the data on your graph. Hint: Be sure to check that all required aspects of a well-formatted graph are included in your answer, and that you have plotted peak wavelength on the vertical axis and temperature on the horizontal axis. iii. A star is measured to have a black-body spectrum that peaks at a wavelength of 0.20 pm. Use your graph to determine the mean surface temperature of the star. Add arrows to your graph to indicate how you used it to determine the temperature. Note: This exercise is intended to test your graph-reading skills. No marks will be awarded for using the sliders in Activity 4.1 to estimate an answer or for using theoretical principles to calculate the temperature. iv. The module notes provide a formula connecting the peak wavelength, A, measured in nanometres (nm), and mean surface temperature, T, measured in kelvin (K). Show how to use this formula to calculate the mean surface temperature of a star whose black-body spectrum peaks at a wavelength of 0.20 pm. Comment on how your answer compares to your result from part (iii). v. Calculate the photon energy that corresponds to the wavelength 0.20 pm. Give your answer using scientific notation, the SI unit for energy and an appropriate number of significant figures. You should assume Planck's constant h = 6.63 x 1034 ] s. b. The Hertzsprung-Russell (HR) diagram shown in Figure 3 below represents the main sequence by a curved band of approximately uniform width. As a consequence, at any given value of the surface temperature, the stars in the main sequence represent a range of stellar luminosities relative to the luminosity of the Sun shown as L/Le. 10 10 109 main sequence B 10 30000 20000 10000 6000 3000 surface temperature /K Figure 3 The Hertzsprung-Russell diagram i. Using the HR diagram (Figure 3) what is the approximate range of relative luminosities covered for a main sequence star at 4000 K? ii. Would this star be most like Mintaka or Betelgeuse? iii. As a star runs out of hydrogen to fuel nuclear fusion in its core, changes within the star usually cause it to leave the main sequence, expanding and cooling as it does so. Would a star with a radius 6 times that of the Sun, but a surface temperature 0.4 times that of the Sun, have a luminosity that is greater than or less than that of the Sun? Show and explain your reasoning. You may assume the surface area of a sphere is A = 4?('?'2. Hint: you will need to consider the proportional effect on stellar luminosity of both the change in the surface area and the change in surface temperature of a star, as implied by Equation 4.2 (see Topic 10: Section 4.1.2). (It isn't necessary to input actual values.) iv. As they run out of nuclear fuel, certain stars undergo very large expansions to become supergiant stars. What is the minimum mass a star must have to become a supergiant