25. Radioactive decay law.

Question 1

Describe the differential form of the law of radioactive decay

Answer 1

Differential form:

• used when decays are observed for a very short time
• **Λ = ∆N/∆t = -λ * N **
• λ = decay constant = [1/s]: describes the probabilty of decay

Question 2

Describe the integral form of the law of radioactive decay

Answer 2

Integral form:

• used when decays are observed for a longer time (h - years)
• N(t) = N₀ * e^−λt = N₀ * 2^-t/T_1/2

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⇒ Λ decreases on the same mode as N

• Λ(t) = Λ₀ * e^−λt = Λ₀ * 2^-t/T_1/2
• During about 10 T the activity decreases to its 1/1000 (e.g GBq->MBq)

Question 3

Define activity

Answer 3

Activity:

• no. of decays of nuclei per time interval
• characterizes the **source **

**→ Λ = ∆N/∆t = -λ * N **in [Bq = Bequerel]

Question 4

Define half-life time

Answer 4

Half-life time:

• time in which the initial no. of undecayed nuclei decreases by half
• characterizes the speed of decay
• depends on the type of isotope

→ T_1/2 = N₀/2

Question 5

Define mean life time

Answer 5

Mean life time:

time in which the initial no. of undecayed nuclei decreases by e

Also the inverse of the decay constant λ.

→ τ = 1/λ = N₀/e

Question 6

Describe the energy levels of different types of radiation and relate Bq levels

Answer 6

Bq levels:

• kBq: level of natural activity
• MBq: in vivo diagnosis
• GBq: carefully to work with
• TBq: radioactivity applied in radiotherapy

Energy levels of radiation:

• eV / aJ: excitation of outer electrons (light)
• keV / fJ: e^- transition between inner e^-, X-ray
• MeV / pJ: decay, nuclear radiation