Hello,

Would you help me to get un-stuck, please? I'm running out of times

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. Spectral type stars data colected Stars - Names | Mean temperature / Kelvin | Wavelength / pm O - Mintaka 40000 0.07 B - Rigel 20000 0.14 A - Sirius 9000 0.32 F - Canopus 7000 041 G - The Sun 5800 0.50 K - Arcturus 4000 0.72 M - Betelgeuse 3000 0.96 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. Rectangular hyperbola Curve of spectral type stars O- mintaka B- Rigel y M F Canops 10.8 K K= Arcturus 0.6. M = Betelgeuse Wavelength / jm 0.4 A 0.2 B about here O 5090 10900 900 20 040 23200 30500 15000 40600 45200 mean Surface temperature / Kiii. 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. See arrows mentioned \"About here\" therefore approximately 12500 K at surface temperature based on my graph. 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). Formula mentioned: Knowing that 1 pm: = 1000 nm So, 0.20 pm: =200 nm Re-aranging the formula to solve T: Inserting the value, T: (125 10* nm . K) - 200 nm = nm cancel eachother out 1.25 x 10* AT o 200 ~ 625 K Therefore, the star mean surface temperarature is approximately 62.5 Kelvin! [ can see that my calculation doesn't agree to the 12500 K showing in my graph! [ could use your imput as to why? 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 10-3] s. Could you help me to get unstuck? 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. main sequence 30000 20000 10000 surface lemperature /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? Same here would you unstuck me please? ii. Would this star be most like Mintaka or Betelgeuse? Most likekly to similar to Berelgeuseiii. 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. 9 You may assume the surface area of a sphere is A = 4d=xr". 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.) Also this questions and the next please? ['m still working on it, but due tomorrow. Hopefully [ would have it done before you do. 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? The last one of questions 4, thank you