The atomic mass unit (symbol: u) is used for indicating mass on an atomic or mol
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The atomic mass unit (symbol: u) is used for indicating mass on an atomic or molecular scale. It is defined as 1/12th of the mass of the carbon atom, so that 1 u = 1.6606 × 1027 kg. In this unit, the mass of the H atom is mH = 1.008 u and the mass of the He atom is MHe = 4.003 u.
1. Given the luminosity of the Sun, and ignoring the energy lost with the solar neutrinos, compute the amount of H that is converted into He in the Sun, every second
2. The figure above shows that the luminosity of the Sun has been increasing almost linearly from 0.7 L when it entered the main sequence, to its current value. Use this approximation to estimate how much H has been converted into He so far by the Sun. Give the solution in units of solar mass and assume an age tSun ' 4.57 × 109 yr for the Sun.
3. What is the total mass lost so far (in solar masses) by the Sun because of H nuclear burning?
4 Can you guess why only the center of the Sun has an increased He abundance as a result of H nuclear burning, while the surface abundance of He is unchanged?
5800 5780 5760 5740 5720 5700 5680 0.9 5660 3 0.8 5640 5620 5600 0.6 Age (10 yr) ema/ FIGURE 11.1 The evolution of the Sun on the main sequence. As a result of changes in its inte dashed composition, the Sun has become larger and brighter. The solid line indicates its luminosity, the line its radius, and the dash-dot line its effective temperature. The luminosity and radius curves relative to present-day values. (Data from Bahcall, Pinsonneault, and Basu, Ap. J., 555, 990, 2001)Explanation / Answer
There are multiple ways Hydrogen gets fused into He and liberates energy in the SUN.
Hydrogen mass = 1.008 u and
that of He = 4.003 u
On the average it takes 4 Hydrogen atoms to convert to He
the mass difference = 1.008*4 - 4.003 = 0.029 u
= 0.029*1.6606e-27 kg
This mass is converted into energy
= mc2 = 0.029^1.6606e-27 *9.0e+16
= 4.33 e-12 J
If L is the Luminocity in J/s
then the number of H-2 atoms burnt = 4L/4.33e-12
= 0.923L e+12 atoms per sec
= 0.923e+12 *3.828e+28 *(1.008*1.6606e-27) kg of H-2 ( L = 3.828e+28)
= 5.91 e+13 kg /s
2. The sun luminosity is increasing linearly and hence we can take the average value for the entire age of SUN
= (1+0.7)/2 = 0.85
rate of buring H-2 = 0.85 L /s
age of SUN = 4.5e+9 yrs
Total amount of H-2 burnt since the start = 4.5e+9*0.85 *5.91e+13 * 365*24*3600
= 7.1289e +30 kg
3. for every 4 H-2 atoms mas lost = 0.029*1.6606e-27 kg
mass of H-2 burnt = 1.008*1.6606e-27 kg
mass lost as energy = 2.877e-2 kg /kg of H-2
mass lost = 7.1289e +30 *2.877e-2 = 7.05e+29 kg
solar mass Ms = 2.0e+30 kg
mass lost so far = 7.05e+29/2.0e+30 = 0.102 Ms
4. Most of the fusion reaction take place in the center of the SUN and it is the hotest spot. Henc the abundance of He is large in the center.
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