Verify the Q values reported in Eqs. 43-13, 43-14, and 43-15. The needed masses are

H11.007825uHe44.002603uH22.014102un1.008665uH33.016049u

Short Answer

Expert verified

The Q values are verified.

Step by step solution

01

Describe the expression for energy

The expression for energy is given by,

Q=-mc2

Here, Q is the energy release in a reaction,m is the mass difference between the parent nuclei and the daughter nuclei, and c is the velocity of light.

02

Verify the Q values

For the first reaction, the energy equation will be as follows.

Q=2m2H-m3H-mnc2.........1

Substitute all the known values in equation (1).

Q=22.014102u-3.016049u-1.008665u931.5MeV/u=3.25MeV

For the second reaction, the energy equation will be as follows.

Q=2m2H-m3H-m1Hc2.........2

Substitute all the known values in equation (2).

Q=22.014102u-3.016049u-1.007825u931.5MeV/u=4.03MeV

For the third reaction, the energy equation will be as follows.

Q=m2H-m3H-mHe-mnc2.........3

Substitute all the known values in equation (3).

Q=22.014102u-3.016049u-1.002603u-1.008665931.5MeV/u=17.59MeV

The calculated Q values are same as the given in equations.

Therefore, the Q values are verified.

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Most popular questions from this chapter

Figure 43-15 shows an early proposal for a hydrogen bomb. The fusion fuel is deuterium,H2. The high temperature and particle density needed for fusion are provided by an atomic bomb “trigger” that involves a U235orPu239fission fuel arranged to impress an imploding, compressive shock wave on the deuterium. The fusion reaction is

52H3He+4He+1H+2n

(a) Calculate Q for the fusion reaction. For needed atomic masses, see Problem 42. (b) Calculate the rating (see Problem 16) of the fusion part of the bomb if it contains 500 kg of deuterium, 30.0% of which undergoes fusion.

Assume that the protons in a hot ball of protons each have a kinetic energy equal tokT, wherekis the Boltzmann constant and Tis the absolute temperature. IfT=1×107K , what (approximately) is the least separation any two protons can have?

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+H113N+γ,Q1=1.95MeV,N1313C+e++v,Q2=1.19,C13+H114N+γ,Q3=7.55,C14+H115O+γ,Q4=7.30,15O15N+e++v,Q5=1.73,C15+H112C+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.

Question: Assume that immediately after the fission of U236according to Eq. 43-1, the resulting Xe140andSr94nuclei are just touching at their surfaces. (a) Assuming the nuclei to be spherical, calculate the electric potential energy associated with the repulsion between the two fragments. (Hint: Use Eq. 42-3 to calculate the radii of the fragments.) (b) Compare this energy with the energy released in a typical fission event.

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