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Chapter 43: Q31P (page 1332)

Calculate the height of the Coulomb barrier for the head-on collision of two deuterons, with effective radius2.1 fm.

Short Answer

Expert verified

The height of the Coulomb barrier for the head-on collision is 170KeV.

Step by step solution

01

Write the given data

  1. Head-on collision of two deuterons.
  2. Effective radius of the barrier, R=2.1fm
02

Determine the formulas for potential barrier

The potential energy of the two charged system is as f U=q1q24蟿蟿蔚0r 鈥︹�� (i)

Here, the distance rbetween the protons when they stop are their center-to-center distance, 2R, and their charges q1andq2are both e.

03

Calculate the height of the Coulomb barrier

Now, consider the conservation of energy for the two-deuteron system, determine the total energy using equation (i) as follows:

2K=U=e24蟺蔚0(2R)

Simplify the equation as:

k=e24蟺蔚0(4R)=9脳109V.mC1.6脳10-19C24(2.1脳10-15m)=2.74脳10-14J=170KeV

This kinetic energy is the required potential energy to cross the barrier.

Hence, the potential height of the Coulomb barrier is 170 KeV.

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Most popular questions from this chapter

Calculate and compare the energy released by (a) the fusion of1.0 kg of hydrogen deep within the Sun and (b) the fission of 1.0 kgofU235in a fission reactor.

Lawson鈥檚 criterion for the d-t reaction (Eq. 43-16) is 苍蟿>1020鈥�s/m3. For the d-d reaction, do you expect the number on the right-hand side to be the same, smaller, or larger?

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