# Radioactivity – problems and solutions

1. Based on the figure below, radioactive activity after decay for 13.86 hours is …

__Known :__

*Half-life (T*_{1/2}*)** **= 6.93 hours*

*Time-lapse (t) = 13.86 hours*

__Wanted:__ radioactive activity

__Solution :__

A* = radioactive activity**, **λ **= the decay constant, N*_{t }*= *The number of radioactive atoms after decaying during a certain time interval*, T*_{1/2 }*= half-life*

**The decay constant :**

**The number of radioactive atoms after decaying during a certain time interval :**

Radioactive activity :

2. Based on the figure below, after the radioactive substance decays for 15 minutes, then the remaining radioactive substance is …

Solution :

*N*_{o}* = The initial amount of the radioactive atoms*

*N*_{t}* = The final amount of the radioactive atoms after decaying during a certain time interval (t)*

*t = time-lapse*

*T 1/2 = half-life*

**Calculate the ****Half-life :**

__Known :__

N_{o} = 8 grams

N_{t} = 2 grams

t = 6 minutes

__Wanted:__ half-life (T 1/2)

__Solution :__

**Calculate the remaining radioactive material :**

__Known :__

*The initial amount of the radioactive atoms (*N_{o}) = 8 grams

*Time-lapse *(t) = 15 minutes

*Half-life* (T 1/2) = 3 minutes

__Wanted:__ the remaining radioactive material (N_{t})

__Solution :__