B - Radioactivity

Question 1

What occurs to the positron after beta plus decay has occurred?

Answer 1

Within 10^-6s, the positron will have travelled several mum and lost nearly all its energy — increasing the chances of a collision with an electron

Since linear momentum is close to 0 then the annihilation radiation must consist of two oppositely directed photons each with an energy 0.511MeV.

Question 2

What conditions do Electron Capture (EC) occur?

Answer 2

Neutron deficient nuclei decay via converting a proton into a neutron BUT whose daughter products are too massive for positron emission and is in direct competition.

Wave function of K shell electrons are closest to the nucleus — hence more probable to be captured than L, M or N.

Question 3

What happens internally during EC once an electron has been captured?

Answer 3

Internal Bremsstrahlung
(Electron decelerates as it becomes captured, releasing the above)

• Due to the acceleration of the negative charge
• would expect continuous distribution with a max energy equal to the transition energy.

Question 4

What is the formula for EC?

Answer 4

AXZ + e- —> AYZ-1 + neutrino_e + gamma + Q (net energy release)

Question 5

What is the internal conversion process that occurs inside the nucleus after EC?

Answer 5

The daughter nucleus is in an excited state following EC

Usually excited states are relieved via gamma ray emission however their is a competing process.

Energy can be transferred to one of the orbiting electrons, which is then ejected (internal photoelectric effect) — the process is accompanied by the characteristic X-ray emission spectra.

If the energy is used to emit electrons from the outer orbitals, these can be used in material diagnostics and are called Auger electrons.

Question 6

Explain what is Resonance absorption

Answer 6

Nucleus can also absorb incident photons at precise energies and cause re-emission (above or fluorescence)

The energy spread is very small and occurs over a small lifetime 10^-12s.

Transition is much broader (up to 0.1eV) due to thermal motions of the nuclei leading to a Doppler-type effect

KEY THEME - decay process followed by other processes to reach stability

Question 7

How to determine if a large nuclei will decay via beta plus or EC?

Answer 7

Beta + requires the energy/mass of for two electrons.

Min mass required is: 0.0010972u
Min energy required is: 1.033MeV

Hence calculate the mass difference (reactants - products) or energy difference and if it’s above then both can happen but if it’s below then it’s only EC

Question 8

Define isotone

Answer 8

Atoms with the same number of neutrons but different number of protons

Question 9

Define isobars

Answer 9

Atoms with the same Mass number A but the combination of Z and N can vary

Question 10

Define isomers

Answer 10

Same A and Z numbers but different energy states

Question 11

Define isodiapheres

Answer 11

Same difference between (N - Z)

Question 12

What are the 4 heavy radioactive decay series? What are their alternative names and why?

Answer 12

1. Thorium series (4n)
   • starts with Th-232
   • final stable nuclide Pb-208
   •nuclides in this series have a Z that is equal and an A that is 4 units less than the parent nuclide
2. Neptunium Series (4n + 1)
   • starts with U-237
   • artificial decay chain
   • less studied and less well known
3. Uranium Series (4n + 2)
   • starts with U-238
   • final stable isotope Pb-206
   • Z is 2 units less and A is 4 units less than parent nuclide
4. Actinium Series (4n + 3)
   • starts with U-235
   •final stable nuclide bismuth (Bi)-209

Question 13

How do you calculate the Q of reaction/ decay? (Two methods)

Answer 13

1. Q = M(reactants) - M(products)
   M(reactants) > M(products) for Q > 0 and for the reaction to occur spontaneously
2. Q = K.E(products) - KE(reactants)