In this problem, you will estimate the duration of the horizontal branch phase f

Question

In this problem, you will estimate the duration of the horizontal branch phase for a 1 M_odot star. Compute the energy released in the net triple alpha reaction 3_4^2 He rightarrow _6^12C. The masses of _2^4He and _6^12C are 4.0026 u and 12.0000 u, respectively, where 1 u = 1.6606 times 10^-27 kg. Assume that at the beginning of the horizontal branch phase, 10% of the mass of the star is in the form of _2^4He in the core. Estimate the total energy released by fusing this amount of helium into carbon via the triple alpha process. Assume that during the horizontal branch phase, L = 100 L_odot. If all of this luminosity is provided by fusion of helium into carbon in the core, how long will the horizontal branch phase last?

Explanation / Answer

a) mass diff = 3(4.0026) - 12.00000 = 7.8 x 10^-3 u

mass diff = 7.8 x 10^-3 x 1.6606 x 10^-27 = 1.2853 x 10^-29 kg

energy = m c^2 = (1.2853 x 10^-29)(3 x 10^8)^2 = 1.166 x 10^-12 J

b) mass of start = 1.99 x 10^30 kg

no. of process = {1.99 x 10^30 / (3 x 4.0026 x 1.6606 x 10^-27 ) } x 10/100

= 9.98 x 10^54

total energy = 9.98 x 10^54 x 1.166 x 10^-12 =1.164 x 10^43 J

(C) L. = 3.846 x 10^26 W

L = 100 x 3.846 x 10^26

t = tottal energy / L = 3.305 x 10^-15 sec

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