Radioactivity

Question 1

Which elements found in nature have unstble nuclei?

Answer 1

Heavy elements (high z) have unequal numbers of protons and neutrons. Too many neutrons makes them unstable.

Question 2

What are the three states in the shell model

Answer 2

• Ground - stable arrangement of nucleons
• Excited - usntable, often transform into other states
• Metastable - unstable but have a relatively long half-life before transforming e.g. 99mTc is metastable state of Tc, they are both isomers.

Question 3

Apha decay

mechanism

use

Answer 3

Alpha decay involves release of He nucleus (2 protons + 2 neutrons), typically occurs with heavy nucleides.

They are not used for imaging becasue they have a very short range (cm in air, um in tissue). Used as a localised radiotherapy treatment. Ra-223.

Question 4

B decay

mechanism

effect on daughter

use & exmaple RN

Answer 4

n -> p⁺ + e^- + electronanti-neutrino (conserving charge and lepton number)

B particle (electron) has a spectrum of energies as the enrgy is shared btween the B and the Ve-. Mean energy is approx.1/3Emax.

B decay can leave the daughter in excited or metastable state.

e. g. Y-90 SIRT imaging, releases no gammas so hard to measure activity but good for imaging.
e. g. Mo99 decay to Tc99m decay to Tc99

Question 5

What is an isomeric transition?

Difference between x-rays and gamma rays?

How is it related to internal conversion?

Answer 5

Decay of metastable nucleide by emission of gamma ray (e.g. Tc99m to Tc99). This is goo because it measn there are no particles emitted.

Gamma rays come from inside the nucleus, x-rays come from outside.

Internal conversion is an alternative to g-ray emission. Energy from unstable nucleus is transferred to orbital electron which is ejected instead of the x-ray. This is usually followed by vacancy filled by outer shell which leads to x-ray emission or auger electron.

Question 6

Electron Capture

mechanism

use

Answer 6

p⁺ + e^- → n + v_e

Electron captured by positron, to form a nueutron and an electron-neutrino, e.g. 123I to 52Te.

Electron capture often results in daughter nucleus that is excited or metastable, making it a gamma emitter.

Use: I123 DaTScan to investigate parkinsons.

Question 7

Positron decay

Mechanism

Answer 7

p⁺ →n + e⁺ + v_e

Proton in nucleus decaus into neutron and positron (and electron neutrino). This reaction is important because the positron often goes on to anihilate with an electron and produce two 190deg separated 511kEv photons (PET).

Question 8

Guess the decay mode

³²P₁₅

¹⁵0₈

Answer 8

³²P₁₅ - Neutron rich (+2), so will beta decay (neutron to proton and electron)

¹⁵0₈ - Neutron deficient (-1), or too many protons, will decay via positron decay. proton to neutron and positron.

Question 9

Match up the decay mechanisms

Neutron excess

Proton excess

Excess protons and neutrons

Answer 9

Neutron excess - B decay

Proton excess - positron decay or EC

Excess protons and neutrons - alpha & fission

Question 10

Activity

eqn & T1/2

unit

How much activity is used for diagnostic imaging

Answer 10

A = N/t (unit = Bq = 1decay/s)

dN/dt = lambda N -> N=No e-^lambda*t

T1/2 = ln2/L

50MBq - 10GBq

Question 11

Determine the effective half life of iodine-131 (t1/2=8.02d) in the human thyroid if it is removed with biological half-life of 80 days.

Answer 11

L_leff = L_phys + L_biol

1/ t ½eff = 1/ t ½ phys + 1/ t ½ biol

1/ t ½eff = (1/8.02) + (1/80) = 0.137

t ½eff = 7.3 days

NB// biological elimination/excretion removes activity as well as physical decay.

NB// the decay constants add.

Question 12

Distribution of measurement of radioactive decay

Answer 12

Poisson : approximated by gaussian.

Mean = SD

SD = sqrtN

Single measurement of N counts, true value is n pm sqrtN. 68% of all measurements fall within mean pm 1SD.

Question 13

How do you decide how long to count for?

How many counts do you need for precission less than pm 1%

Answer 13

• Precision characterised by CoV = SD/Mean = sqrtN/N = 1/sqrtN
• 1/sqrtN = 0.01 -> n = 10 000

Question 14

Sample counted for 25 minutes and measured 400 CPM.

What is the σ of the count rate?

Answer 14

• DON’T JUST SQUARE ROOT THE RATE
• Total counts = 400*25 = 10000 -> SD = 100
• Total counts = 10000 pm 100 counts
• SDrate = sqrtN/t = sqrt(rate*t)/t = sqrt(rate/t)
• Count rate (divide by mins) = 400 pm 4 CPM

Get the error on the total counts then divide back to get error on rate.

Question 15

A sample counted for 10 min yields 35500 counts. A 1 min background measurement yields 45 counts. Find the net counting rate and standard deviation.

Answer 15