Mathematics of Nuclear Decay

Question 1

How do we measure or quantify the number of nuclei?

Answer 1

It is difficult to measure or quantify the number of nuclei, N, in a sample and an easier quantity to work wi the activity of the sample.

Question 2

What is the unit for 1 decay / second?

Answer 2

Becqurel (Bq)

Question 3

How can you measure the number of decays per second (as a way to measure/quantify the number of nuclei in a sample)?

Answer 3

The number of decays per second also known as the “activity of the sample” can be measured through the decay products that emerge.

e.g. - photons produced from an isomeric transition, etc

Question 4

Define Activity, A

Answer 4

The number of decays per second

Question 5

What is the equation for the Activity, A?

Answer 5

A = dN / dt

Question 6

What is the solution for Activity, A = dN / dt ?

Answer 6

A(t) = the activity at some time t

A0 = the activity at time 0

Question 7

What is the SI unit for activity (decays per second)?

Answer 7

Becquerel (Bq)

Question 8

What is the another uniy for activity (decays per second)?

Answer 8

Curie (Ci) = 3.7 x 10^10

or

1 mCi = 3.7 x 10^7

or

1 Ci = 3.7 x 10^10

Question 9

What does conceptually half-life indicates?

Answer 9

the time in which the activity of an isotope reaches half of its initial activity

Question 10

What is the half life equation?

Answer 10

Question 11

What is the equation of half life and decay constant lambda?

Answer 11

t(h) (half life) = 0.693 / lambda

Question 12

What determines the decay constant?

Answer 12

stability of the nucleus, less stable nuclei will have a larger decay constant, lambda, which turns into a shorter half-life.