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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=q1q24ττε0r …… (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=e24πε0(2R)

Simplify the equation as:

k=e24πε0(4R)=9×109V.mC1.6×10-19C24(2.1×10-15m)=2.74×10-14J=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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