How does the mean density of a 1.5 Mo neutron star compare to a carbon nucleus? Assume the carbon nucleus has a radius r = 3 × 10–15 m.
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- The exponential drop in the brightness of supernova 1987A was due to the decay of 56Ni (t1/2 = 6.1 days) → 56Co (t1/2 = 77.1 days) → 56Fe. If the energy were primarily due to the decay of 56Ni, what falloff in brightness by the end of 300 days would we expect? What if it were due to the energy in the decay of 56Co? The actual data showed a decrease in brightness by a factor of about 100 after 300 daysAssume that the laws of Newtonian mechanics and Newtonian gravity still hold for a neutron star, what approximately is the escape velocity at the surface of a 1.4 solar mass neutron with a radius of 10 km? A. 2×108 m/s B. 108 m/s C. 1.5 ×108 m/s D. 2.5 ×108 m/sFind the wavelength of peak intensity for a hot 45000 K star that emits thermal radiation.
- what is the answer for sub item (b) if the radius of the neutron star is 69.601 km? (express your answer in the proper SI unit ans without scientific notation)a) b) Electron degeneracy pressure in a white dwarf star, of uniform density p, in the nonrela- tivistic case is given by Pwd ħ² 3memp 25/305/3 where symbols have their usual meanings. Using the result that the central pressure in a star, of radius R and uniform density, under gravitational attraction is given by Pc = Gp² R², derive an expression for the radius Rwd of a white dwarf in terms of its mass M, in the case of nonrelativistic electron degeneracy. Using your result, briefly discuss the limitations of your expression for the radius, in the context of white dwarfs of increasing mass. Consider a white dwarf, mass M, radius Rwd and temperature T, consisting entirely of helium nuclei and electrons. Show that the internal thermal energy of the ions alone is given by 3 M Eth= -kT, 8 mp where mp is the proton mass. White dwarfs initially have a very high temperature when they form, and then cool by radi- ation. Derive a differential equation for the rate of change of the temperature…The typical core-collapse supernova has an energy budget of about 1046 J. This energy comes from the gravitational potential energy of an inner core with mass Mic, which collapses from an initial radius of 5 x 106 m down to the final radius of 50 km. Estimate Mic, in solar masses, for this to be a realistic energy source of the core-collapse supernova. You may assume that the density before the collapse is uniform. Discuss briefly how a Type la supernova is different from a core-collapse supernova from a massive star?
-  Q/ b) Vega Star of radius (1.6832) million km emit a) thermal radiation as a black body radiation at temperature of (18500 K). Calculate the Luminosity of this star. [o is Stefan-Boltzmann constant = 5.67 *x 10-5 erg cm-2 K-4 s-1]= 2000 K and a radius of R, A young recently formed planet has a surface temperature T Jupiter radii (where Jupiter's radius is 7 x 107 m). Calculate the luminosity of the planet and 2 determine the ratio of the planet's luminosity to that of the Sun.A particle has γ=9,681. Calculate c-v in m/s. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation.
- Calculate the energy Er, in megaelectronvolts (MeV), released in the following nuclear fission reaction: Cm(250) + n → Se(92) + Sm(153) + 6n The atomic masses are Cm(250)=250.078357 u, Se(92)=91.949926 u, and Sm(153)=152.922097 u. Er = ? MeVA star collapses onto a neutron star. If its original radius is 7x105 km, by what factor will its spin rate increase?A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.