# How are nuclear reactions autocatalytic?

### 21. Nuclear Physics

1. p + e → n
Is the reaction equation correct? If it's not correct: fix it.
Can the reaction go in the specified direction?

Solution:

The balance of the leptonic charge is incorrect. Adding a neutrino on the right side fixes the reaction.

If the starting particles are at rest, the reaction cannot run in the specified direction, because the rest energy of proton and electron together is smaller than that of the neutron.

2. ﻿ Is the reaction equation correct? If it's not correct: fix it.

Solution:

The balance of the leptonic charge is incorrect. Adding an antineutrino to the right side fixes the reaction.

3. Is the reaction equation correct? If it's not correct: fix it.
In which direction is the reaction going?

Solution:

The balance of the leptonic charge is incorrect. Adding an antineutrino to the right side fixes the reaction.
Reaction direction: from left to right (calculate from table values)

4. A lithium nucleus is supposed to arise from a deuterium nucleus and a tritium nucleus. Is the following reaction equation correct?
If not, complete them. Is the reaction going in the desired direction?

Solution:

The balance of the leptonic charge is incorrect. Adding an antineutrino on the right side fixes the reaction.
The total rest energy of the particles on the left is 5.02 pJ greater than that of the particles on the right (calculate with table). So the reaction can run.

5. The amount of an unstable nuclide decreases to one eighth in 27 days. What is the half-life?

Solution:

9 days

6. An unstable nuclide is examined, namely an amount of 0.01 mol. It can be seen that around 15,000 nuclei disintegrate every second. Give a rough estimate of the half-life. Express the result in years. 7. One examines two different nuclides A and B, namely equal amounts. One measures for two minutes and finds that during this time 22 nuclei of A decay and 19 of B. What can you say about the half-lives of the two substances?

Solution:

The half-lives are similar. But one cannot decide whether A or B has the longer half-life.

8. What is the reaction in the sun?
Why does it walk in the sun but not on the earth?

Solution: The reaction is severely inhibited. She walks in the sun because the temperature is high there. However, it still runs very slowly there too.

9. ﻿﻿ Solution: 10. Describe the reaction that takes place in a nuclear reactor in which a uranium nucleus breaks into two parts. (You don't need to give a reaction equation.)

Solution:

Uranium or plutonium nuclei disintegrate into two parts, the size of which is not very different. The reaction is severely inhibited. Neutrons act as a catalyst. Since the reaction produces neutrons, it is an autocatalytic reaction.

11. The turnover rate of nuclear reactions is usually very small. How can a nuclear reaction be accelerated? Where do such accelerated reactions take place?

Solution:

Like a chemical reaction: by increasing the temperature or by a catalyst. The acceleration of the reaction by increasing the temperature is used in the stars and in the fusion reactor. The catalytic effect of neutrons is used in the conventional nuclear reactor.

12. Which particles do the nuclei of the three isotopes of hydrogen consist of (specification of the content formula is sufficient)?

Solution: 13. How does a particle differ from its antiparticle? In what do particles and antiparticles agree?

Solution:

equal: masses of fame; different: opposite signs of electrical, baryonic and leptonic charge

14. Name properties of the neutrino. Where do neutrinos appear?

Solution:

Very small rest mass, electrical and baryonic charge equal to zero, leptonic charge equal to one. They arise in nuclear reactions, especially in the sun. Detection is difficult because they only react very weakly with other particles.

15. Explain the terms element, nuclide and isotope.

Solution:

Element: characterized by the number of protons, there are around 100 different ones
Nuclide: characterized by the number of protons and the number of neutrons, there are around 2000
Isotopes: the different nuclides of an element

16. Make a table listing the electrical, baryonic and leptonic charges of the following particles: photon, electron, antielectron, neutrino, antineutrino, proton, antiproton, neutron and antineutron (the electrical charge in units of elementary charge ).

17. What is the separation energy of a core?

18. Why is it so hot inside the sun?
Why does the sun “live” so long?

Solution:

It is so named because the inside of the sun is very well insulated from heat.
The reaction is very slow because the temperature for a nuclear reaction is still very low.

19. How is it that the sun doesn't explode?

Solution:

When entropy is supplied, the sun becomes larger and colder at the same time. This reduces the conversion rate.

20. A core is broken down into its components. Are the components heavier or lighter together than the core? Justify.

Solution:

Energy is needed for dismantling, i.e. it is fed into the system. Because of E. = k · m the mass of the system increases.

21. Why do you need very reliable safety precautions in a nuclear reactor?

Solution:

Because after the nuclear fission reaction has been switched off, the reactor still produces heat through subsequent actions. It must be possible to dissipate this so that the reactor core does not melt.