# Difference between revisions of "Solutions 5"

From mn/safe/nukwik

(→Particles and Nuclear Reactions) |
|||

Line 81: | Line 81: | ||

<br> | <br> | ||

− | |||

− | |||

<br> | <br> | ||

− | + | [[Category:Solved Problem]] | |

− |

## Revision as of 12:58, 26 June 2012

# Particles and Nuclear Reactions

###### Return to Problem Solving Sets

**1:**

- Thermal neutrons have a kinetic energy of about 0.025eV
- Fast neutrons are “braked” with elastic collisions with particles with the same size as the neutrons. A moderator also needs to have a low cross-section for absorbing neutrons.
- A moderator is a material that brakes the neutrons, for instance H
_{2}O, D_{2}O, C, Be. A neutron absorbent catches the neutrons and reacts with the neutron. Good absorbants are borium and gadolinium. - From the nuclide carte we can see that
^{3}He has a high cross-section for the n,p-reaction. - The reaction
^{3}He+n^{3}H^{+}+^{1}H(+^{2}e^{-}). The charged particles from the reaction creates more ionisations when they travel towards the anode and the cathode, this gives a electric signal. - The Q-value from the reaction is 763 keV, the reaction is exothermic.
^{3}H^{+}and^{1}H^{+}is created.- The two products in the reaction receives opposing recoils 180 degrees. Conversion of momentum m
_{1}v_{1}=m_{2}v_{2}gives:

**2:**

- Q-Value 2.224 MeV

- And 3. The energy of the deuterium is not calculated relativistic but the γ-ray is completely relativistic, we then get:

Inserting the energy of the deuterium we get:

we know that

_{}

solving for this:

**3:**

Q-Values

^{40}Ca: M(^{40}Ca)+M(α)-M(^{44}Ti)=5.13 MeV

^{52}Cr: 7.61 MeV

^{56}Fe: 6.29 MeV

^{58}Ni: 3.37 MeV

**4:**

For ground state transitions assuming zero momentum to the neutrino

- 0.16 MeV

- 0.78 MeV

- 1.655 MeV subtracting the mass of a electron and a positron we end up at 0.633 MeV.

- β
^{-}:0.579 for^{64}Zn, β^{+}: 0.653 MeV for^{64}Ni. - The cause of this effect is the even-even/odd-odd addition to the energy

^{228}Ra is created with disintegration of^{232}Th:^{232}Th^{228}ra + α +Q this gives

M(^{228}Ra) = M(^{232}Th)-M(α)-Q

All of the natural thorium that exist is^{232}Th. The mass that is given for thorium is therefore more or less equal to the mass^{232}Th 232.0381 u. It is much the same for helium where the mass is 4.002602 u. To find M(^{228}Ra) we need to find the Q-value. The excess energy (Q-value) is distributed as kinetic energy on the products^{228}Ra and alpha. The alpha particle has very little mass compared to^{228}Ra, and the alpha particle by conversion of momentum will receive almost all the kinetic energy:

_{α} is know ( using the most powerful α for transition to ground state), and the Q value is found with: This gives

**5: **

** 6:**

- Q-value is 2.789 MeV

**7:**

- 1 GBq
^{89}Zr = 4.1 10^{14}atoms, there must be created 1.9 10^{10}per second - Yttrium is a mono isotope, it is only
^{99}Y is the only natural isotope. Therefore there is no need to purify the sample for other isotopes.