17.2 (a) Use the fact that f [2³/(e² - 1)] dz = π/15 to show that the total radiant energy emitted per second by unit area of a blackbody is 27³KT4/15c²h³. Note that this quantity is propor- tional to T4 (Stefan's law). (b) The sun's diameter is 1.4 X 10⁰ m and its effective surface temperature is 5800 K. Assume the sun is a blackbody and estimate the rate of energy loss by radiation from the sun. (c) Use E = mc2² to calculate the relativistic mass of the photons lost by radiation from the sun in 1 year.
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- The sun has a radius of 6.959 × 108 m and a surface temperature of 5.81 x 10° K. When the sun radiates at a rate of 3.91 x 1026 W and is a perfect emitter. What is the rate of energy emitted per square meter? Stefan-Boltzmann constant is 5.67 x 10-8 J/s-m2 K4 a) 5.6 x 107 W/m2 b) 12.8 x 107 W/m2 c) 6.4 x 107 W/m2 25.6 x 107 W/m2 5.6 x 1017 W/m2Calculate the amount of radiation emitted for a unit surface (2 m2) for black ball at 53°C and £≈0.96 Express your answer SI units (in W).The churge deisity asphre of glvn काि hब ऊगर पु pc,@,¢)= Krcos (20) sind pus (oe (Kunstant) of the sphee कdड मिण्र नजय cos 2XSinxdx= Te(-4x+4Sin&x-5h 4x calulute the t p ot dipok manut may need the followilag intyoad you nou b. Find the leading exparsion af the potarial at points r away from term in the multipok the
- Use Wein's law to determine the wavelength corresponding to the peak of the black body curve (a) in the core of the Sun, where the temperature is 10^7, (b) in the solar convection zone (10^5), and (c) just below the solar photosphere (10^4K). What form (visible, infrared, X-ray, etc.) does radiation take in each case?1. The mass of the Sun is about 2x10³0 kg. The Sun was about 72% hydrogen when it first formed. About 11% of the total amount of the Sun's hydrogen is available for fusion within the Sun's core. [3 points] (a) What is the total mass of hydrogen available for fusion, in kg? (b) The Sun fuses about 600 billion kg of hydrogen each second. Calculate how long the Sun's initial supply of hydrogen can last. Give your answer in both seconds and years. Hint: use the result you calculated in part (a). (c) We know that our Solar System is about 4.5 billion years old. Using your calculation above, how much longer do we have until the Sun runs out of hydrogen?/dsinė A beam of electrons is shot towards a material X with a crystalline structure. A diffraction pattern is observed corresponding to a distance d=0.15 nm. between two adjacent Bragg planes. The electrons are each sent in with a kinetic energy of 51.900000000000006 eV. Part a) Find the de Broglie wavelength in nanometres of an electron incident on the material X.
- The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law. Calculate the peak wavelength of a bluish-white star that radiates at temperature 20000 K. a) 145 nm b) 100 nm c) 114 nm d) 155 nmIf the radius of the sun is 7.001×105 km, what is the average density of the sun in units of grams per cubic centimeter? The volume of a sphere is (4/3)π r3. The sun is a sphere with an estimated mass of 2.00×1030 kg. What exactly is the conversion process for this?Please solve accurate. Thanks
- A)The star 58 Eridani is a feint but naked-eye star similar to the Sun. Suppose that you are observing this star in the night sky without a telescope. Ignoring any interstellar extinction or atmospheric absorption, approximately how many photons per second arrive at your retina? Show all steps in calculation . B) The Mid-infared Instrument (MIRI , camera and spectrograph ) on the James Webb Space Telescope operates in the band 5-28 µm . For 58 Eridani , approximatley how many photons per second can be used by this instrument ? Assume that MIRI takes all the photons from the full JWST mirror . Show all steps in calcultation . Describe breifly two or three other factors which play a role in determining the sensetivitu of an instrument such as MIRI ?2 of 7 Question A2 a) Calculate the mass loss rate of the Sun M due to the solar wind flow. Assume average properties of the solar wind of number density 6 protons cm³, and a flow speed of 450 km s-1. Express your answer in units of both kg per year, and solar masses per year. b) Suppose the solar wind flow is perfectly radial. Calculate the expected rate of change of solar rotation frequency dw at the present time, based on conservation of angular momen- tum. Give your answer in units of rad s-1 y-1 (i.e., radians per second per year) and also in terms of fractional change per year, i.e., 1 du. w dt' Use a current solar rotation period of P = 25.38 days to calculate the current angular frequency of rotation w. The moment of inertia of a uniform sphere is MR². You can assume that the radius of the Sun is approximately constant, and the change in its moment of inertia due to the solar wind is only due to the mass loss. Page 3 c) By observing the rotation period of stars similar to the…a.Calculate the mass loss rate of the Sun M˙ due to the solar wind flow. Assume averageproperties of the solar wind of number density 6 protons cm−3, and a flow speed of 450 kms−1. Express your answer in units of both kg per year, and solar masses per year. b.Suppose the solar wind flow is perfectly radial. Calculate the expected rate of change ofsolar rotation frequency dω/dt at the present time, based on conservation of angular momentum. Give your answer in units of rad s−1 y−1(i.e., radians per second per year) and alsoin terms of fractional change per year, i.e., 1/ωdω/dt .Use a current solar rotation period of P = 25.38 days to calculate the current angularfrequency of rotation ω. The moment of inertia of a uniform sphere is 2/5 MR2. You canassume that the radius of the Sun is approximately constant, and the change in its momentof inertia due to the solar wind is only due to the mass loss. c.By observing the rotation period of stars similar to the Sun, it is inferred that their…