Physics, 08.09.2020 14:01 jagarcia2024
A neutron is confined in a 10-fm-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 2.0 fm from the edge of the nucleus?
P = %
Answers: 3
![\Phi (x) = \sqrt{ \frac{2}{d} } sin [\frac{\pi x}{d} ]](/tpl/images/0745/6628/c0d08.png)
![=2 * \int\limits^2_0 { |\sqrt{ \frac{2}{d} } sin [\frac{\pi x}{d} ]|^2} \, dx](/tpl/images/0745/6628/bc1de.png)
![= \frac{4}{d} \int\limits^2_0 { | sin [\frac{\pi x}{d} ]|^2} \, dx](/tpl/images/0745/6628/c4585.png)
![[sin(\theta)]^2 = \frac{1- cos (2\theta )}{2}](/tpl/images/0745/6628/67b98.png)
![= \frac{4}{d} \int\limits^2_0 { |\frac{1 - cos [\frac{2\pi x}{d} ]}{2} |} \, dx](/tpl/images/0745/6628/ddfaf.png)
![=\frac{2}{d} [x - \frac{sin [\frac{2\pix}{y} ]}{[\frac{2\pi}{d} ]} ]\ |\left 2} \atop {0}} \right.](/tpl/images/0745/6628/44af1.png)
![= \frac{2}{d} [2 - \frac{sin[\frac{2\pi (2)}{d} ]}{\frac{2\pi}{d} } ]](/tpl/images/0745/6628/cf0e8.png)
![= \frac{2}{10} [2 - \frac{sin[\frac{2\pi (2)}{10} ]}{\frac{2\pi}{d} } ]](/tpl/images/0745/6628/7db90.png)
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A neutron is confined in a 10-fm-diameter nucleus.
If the nucleus is modeled as a one-dimensional r...
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