Question 7: Radium has half-life of about 1600 years. If the universe was formed five billion or more years ago, why is there any radium left now?
If there still exists Radium in the universe, there are two main reasons for that.
(1) The law of radioactive decay is
N = N0e-λ t … … … (1)
Here N0 is the initial number of isotopes and N is the number of isotopes decayed in time t. However, this equation shows that for a complete decay of the N0 isotopes, an infinite time is required. Since the time of the formation of earth is not infinite, no matter how long it is, therefore, the Radium still exists in nature. If the earth was formed 5 billion years (5000000000) ago, there would be 3125000 half-lifes of Ra and according to the above equation, there would still be some Ra on the earth. It will be as far as a single atom of Ra is there.
(2) Radium is constantly being produced on the earth due to the decay of uranium and thorium and the amount of Ra is constantly added with. Therefore, there is still Ra in a sufficient amount on earth.