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Chapter 40: Q. 34 (page 1176)

A neutron is confined in a 10fm-diameter nucleus. If the nucleus is modeled as a one-dimensional rigid box, what is the probability that a neutron in the ground state is less than 2.0fm from the edge of the nucleus?

Short Answer

Expert verified

The probability is9.72%.

Step by step solution

01

Given information 

We know that ,

Diameter =10fm

Neutron at positon =2fm

We have to find the probability of the ground state.

02

Simplify

In general for the ground state for any particle the wave function is given by,

蠁(x)=2Lsin蟺虫L

Then, the probability is defines as below with factor of 2 due to neutron is distributed symmetrical around the nucleus.

P=2鈭�00.2fm蠁(x)2dxP=2鈭�00.2fm2Lsin2蟺虫LdxP=4L鈭�00.2fm(1-cos2蟺虫L)dxP=4Lx-sin2蟺虫LL2蟺02fmP=410fm2fm-sin2蟺脳2fm10fm10fm2蟺P=0.0972P=9.72%

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