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# Energy of Particles in the Nucleus

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a) Suppose that the potential seen by a neutron in a nucleus can be represented (in one dimension) by a square well of width 10^12 cm with very walls. What is the minimum kinetic energy of the neutron in this potential, in Mev?
b) Can an electron be confined in a nucleus? Answer the question using the following outline or some other method?

i) Using the same assumption as in a) - that the nucleus can be represented as a one-dimensional infinite square well of width 10^12cm - calculate the minimum kinetic energy, in MeV. of an electron bound within the nucleus.

ii) Calculate the approximate coulomb potential energy, in MeV, of an electron at the surface of the nucleus, compared with its potential energy at infinity. Take the nuclear charge to be +50e.

iii) Is the potential energy calculated in ii) sufficient to bind the electron of the kinetic energy calculated in i)?

"An introduction to Quantum Physics" by French and Taylor.

https://brainmass.com/physics/binding-energy/energy-particles-nucleus-530987

#### Solution Preview

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a) Suppose that the potential seen by a neutron in a nucleus can be represented (in one dimension) by a square well of width 10^12 cm with very walls. What is the minimum kinetic energy of the neutron in this potential, in Mev?
b) ...

#### Solution Summary

The solution determines the energy of particles in the nucleus.

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## Collision of alpha particle with lead nucleus

An alpha particle with kinetic energy 14.0 MeV makes a collision with a lead nucleus, but it is not "aimed" at the center of the lead nucleus, and has an initial nonzero angular momentum (with respect to the stationary lead nucleus) of magnitude L=(p0)b, where p0 is the magnitude of the initial linear momentum of the alpha particle and b = 1.40×10^-12 m. (Assume that the lead nucleus remains stationary and that it may be treated as a point charge. The atomic number of lead is 82. The alpha particle is a helium nucleus, with atomic number 2.)

What is the distance of closest approach?

Repeat for b = 1.40×10^-13 m.

Repeat for b = 1.30×10^-14 m.

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