The theory of radioactive decay

Question 1

How is radioactive decay unpredictable?

Answer 1

• each nucleus has an equal probability of decay
• this is why more nuclei decay per second when the mass of radioactive nuclei is larger

Question 2

What is the change of number of nuclei propotional to of a particular isotope?

Answer 2

• number of nuclei remaining
• the time interval

Question 3

What is the equation for the rate of disintergration

Answer 3

• (ΔN / Δt) = - λ N
  
  • λ = the decay constant

Question 4

What is the equation for the remaining number of nuclei in n half-lives?

Answer 4

N = 0.5ⁿ N₀

Question 5

Rearrange the equation:

N = N₀e^-λt

Answer 5

• N / N₀ = e^-λt = e^(1/λt)
• N₀ / N = e^λt
• ln ( N₀ / N ) = λt
• can also be used for activity and mass

Question 6

What is the decay constant?

Answer 6

• λ
• the probability of an individual nucleus decay per second

Question 7

if there are 10000 nuclei present and 300 decay in 20s, what is the decay constant? Pay attention to the definition

Answer 7

• (300 / 10000) / 20 = 0.0015s^-1
• 300 / 10000 is the probability of a nucleus decaying in 20s
• divide by 20 to find the the probability of the nucleus decaying in a second
  *

Question 8

What is the equation for the probability of decay per unit of time (λ), using (N and T)

Answer 8

(ΔN / N) / Δt

Question 9

What is the equation that link the half life to the decay comnsant?

Answer 9

• T_1/2 = ln2 / λ = 0.693 / λ