## Related questions with answers

If ${ }^{235} \mathrm{U}$ captures a neutron to form ${ }^{236} \mathrm{U}$ in its ground state, the energy released is $B\left({ }^{236} \mathrm{U}\right)-B\left({ }^{235} \mathrm{U}\right)$. (a) Prove this statement. (b) Use the binding-energy formula to estimate the energy released, and compare with the observed value of $6.5 \mathrm{MeV}$. (Note: We have assumed here that ${ }^{236} \mathrm{U}$ is formed in its ground state, and the $6.5 \mathrm{MeV}$ is carried away, by a photon, for example. An important alternative is that ${ }^{236} \mathrm{U}$ can be formed in an excited state, $6.5 \mathrm{MeV}$ above the ground state. This excitation energy can lead to oscillations that cause the nucleus to fission.)

Solution

Verified**(a)** The binding energy of $^{236}\text{U}$ is the energy needed to separate all of the $92$ protons and $144$ neutrons from its nucleus. It is energy coming from the difference between the total mass of its individual constituents and the mass of the nucleus as a whole. The binding energy can also be written as:

$B(^{236}\text{U})=S_n(92,144)+B(^{235}\text{U})$

That is, the binding energy is equal to the sum of the energy needed to remove a neutron and the binding energy of what remains in the nucleus.

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (1 more)Randall D. Knight#### Modern Physics for Scientists and Engineers

2nd Edition•ISBN: 9780138057152Chris D. Zafiratos, John R. Taylor, Michael A. Dubson#### Mathematical Methods in the Physical Sciences

3rd Edition•ISBN: 9780471198260Mary L. Boas#### Fundamentals of Physics

10th Edition•ISBN: 9781118230718 (2 more)David Halliday, Jearl Walker, Robert Resnick## More related questions

1/4

1/7