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Chapter 43: Q44P (page 1332)

Assume that the core of the Sun has one-eighth of the Sun’s mass and is compressed within a sphere whose radius is one-fourth of the solar radius. Assume further that the composition of the core is 35% hydrogen by mass and that essentially all the Sun’s energy is generated there. If the Sun continues to burn hydrogen at the current rate of 6.2×1011kg/s, how long will it be before the hydrogen is entirely consumed? The Sun’s mass is 2.0×1030kg.

Short Answer

Expert verified

The required time is 5×109years.

Step by step solution

01

Describe the expression for the time needed for hydrogen to burn

The expression for the time needed for hydrogen to burn is given by,

t=mdmdt.......(1)

02

Find the need for hydrogen to burn

Substitute all the known values in equation (1).

t=0.35182×1030kg6.2×1011kg/s36524×60×60=5×109years

Therefore, the required time is 5×109years.

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Most popular questions from this chapter

The fission properties of the plutonium isotope Pu239are very similar to those of U235. The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1.0 kg of purePu239 undergo fission?

During the Cold War, the Premier of the Soviet Union threatened the United States with 2.0 megaton Pu239warheads. (Each would have yielded the equivalent of an explosion of 2.0 megatons of TNT, where 1 megaton of TNT releases 2.6×1028MeVof energy.) If the plutonium that actually fissioned had been 8.00% of the total mass of the plutonium in such a warhead, what was that total mass?

In certain stars the carbon cycle is more effective than the proton–proton cycle in generating energy.This carbon cycle is

C12+H1→13N+γ,Q1=1.95MeV,N13→13C+e++v,Q2=1.19,C13+H1→14N+γ,Q3=7.55,C14+H1→15O+γ,Q4=7.30,15O→15N+e++v,Q5=1.73,C15+H1→12C+4He,Q6=4.97

(a) Show that this cycle is exactly equivalent in its overall effects to the proton–proton cycle of Fig. 43-11. (b) Verify that the two cycles, as expected, have the same Q value.

(See Problem 21.) Among the many fission products that may be extracted chemically from the spent fuel of a nuclear reactor is Sr90(T1/2=29y). This isotope is produced in typical large reactors at the rate of about 18 kg/y. By its radioactivity, the isotope generates thermal energy at the rate of 0.93 W/g. (a) Calculate the effective disintegration energy Qeffassociated with the decay of a Sr90nucleus. (This energy includes contributions from the decay of the Sr90daughter products in its decay chain but not from neutrinos, which escape totally from the sample.) (b) It is desired to construct a power source generating 150 W (electric power) to use in operating electronic equipment in an underwater acoustic beacon. If the power source is based on the thermal energy generated by 90Sr and if the efficiency of the thermal–electric conversion process is 5.0%, how muchSr90is needed?

Pick the most likely member of each pair to be one of the initial fragments formed by a fission event:

(a) Sr93or Ru93

(b) Gd140or I140,

(c) Nd155 or Lu155.

(Hint: See Fig. 42-5 and the periodic table, and consider the neutron abundance.)
See all solutions

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