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Chapter 40: Q. 43 (page 1177)

Showed that a typical nuclear radius is 4fm As you’ll learn in Chapter 42, a typical energy of a neutron bound inside the nuclear potential well isEn=-20MeV. To find out how “fuzzy” the edge of the nucleus is, what is the neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius?

Short Answer

Expert verified

The neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius is1.02fm.

Step by step solution

01

Given Information

We need to find the neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius.

02

Simplify

The distance ηis given as the equation:

η=h2mU0-E

Since the neutron's energy is 20MeVunder U0, so the U0-Ehas a value of 20MeV, and the distance is:

η=1.05×10-34Js21.67×10-27kg20×106eV×1.6×10-19JeVη=1.2×10-15m=1.02fm

The penetration distance is 25%of the nuclear radius.

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FIGURE Q40.7shows two possible wave functions for an electron in a linear triatomic molecule. Which of these is a bonding orbital and which is an antibonding orbital? Explain how you can distinguish them.

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