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Fundamentals Of Physics
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Short Answer

(a) Calculate the rate at which the Sun generates neutrinos. Assume that energy production is entirely by the proton-proton fusion cycle. (b) At what rate do solar neutrinos reach Earth?

a) The rate at which the Sun generates neutrinos is 1.8×1038s-1 .

b) The rate at which the solar neutrinos reach Earth is 8.2×1028s-1 .

See the step by step solution

Step by Step Solution

Step 1: Describe the expression for the rate

The expression for the rate at which the Sun generates neutrinos is given by,

Rv=2PQ .......(1)

Step 2: Find the rate at which the Sun generates neutrinos(a)

The energy per fusion is Q=26.7 MeV , and the power of the sun is P=3.9×1026W .

Substitute all the known values in equation (1).

Rv=23.9×1026W26.7 MeV =23.9×1026W26.7 MeV1.602×10-13J/MeV =1.8×1038s-1

Therefore, the rate at which the Sun generates neutrinos is 1.8×1038s-1 .

Step 3: Find the rate at which the solar neutrinos reach Earth(b)

Let Rv,e be the rate at which the solar neutrinos reach the earth,d is the distance between the earth and the sun and r is the radius of the earth.

The expression of the rate is given by,

Rv,e=Rvπr24πd2 =Rvr24d2 .......(2)

The radius of the earth is r=6.4×106 m , and the distance between the earth and the sun is d=1.5×1011m .

Substitute all the known values in equation (2).

Rv,e=1.8×1038s-16.4×106m221.5×1011m2 =8.2×1028s-1

Therefore, the rate at which the solar neutrinos reach Earth is 8.2×1028s-1 .

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