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Chapter 1: Q31P (page 1)

Calculate the height of the Coulomb barrier for the head-on collision of two deuterons, with effective radius 2.1 fm.

Short Answer

Expert verified

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

Step by step solution

01

Write the given data

a) Head-on collision of two deuterons.

b) Effective radius of the barrier, R = 2.1 fm

02

Determine the formulas for potential barrier

The potential energy of the two charged system is as follows:

Uq1q24ττε0r …… (i)

Here, the distance rbetween the protons when they stop are their center-to-center distance, 2R, and their chargesq1andq2 are both .

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=e24ττε02RSimplifytheequationas:K=e24πε04R=9×109V.mC1.6×10-19C242.1×10-15m=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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