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

Write the given data

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

Determine the formulas for potential barrier

The potential energy of the two charged system is as f $U = \frac{q_{1} q_{2}}{4 {ττε}_{0} r}$ …… (i)

Here, the distance rbetween the protons when they stop are their center-to-center distance, 2R, and their charges $q_{1} and q_{2}$ are both e.

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:

$2 K = U = \frac{e^{2}}{4 {πε}_{0} (2 R)}$

Simplify the equation as:

$k = \frac{e^{2}}{4 {πε}_{0} (4 R)} = \frac{(9 \times 10^{9} \frac{V . m}{C}) {(1.6 \times 10^{- 19} C)}^{2}}{4 (2.1 \times 10^{- 15} m)} = 2.74 \times 10^{- 14} J = 170 KeV$

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

Short Answer

Step by step solution

Write the given data

Determine the formulas for potential barrier

Calculate the height of the Coulomb barrier

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