In 1976 a research hospital bought half a gram of radium for cancer research. Assuming the hospital is still exists, how much of this radium will the hospital have in the year 6836 if the half-life of radium is 1620 years?

Question

In 1976 a research hospital bought half a gram of radium for cancer research. Assuming the hospital is still exists, how much of this radium will the hospital have in the year 6836 if the half-life of radium is 1620 years?

Answer 1

To determine how much of the radium the hospital will have in the year 6836, we need to calculate the number of half-lives that have passed since 1976.

The half-life of radium is given as 1620 years, which means that after every 1620 years, the amount of radium will be reduced to half of its original quantity.

Let's calculate the number of half-lives that have occurred from 1976 to 6836.

Step 1: Calculate the number of years passed from 1976 to 6836.
6836 - 1976 = 4860 years

Step 2: Divide the total number of years by the half-life to calculate the number of half-lives.
4860 / 1620 = 3

So, we find that three half-lives have occurred during this time period.

Now, let's calculate the amount of radium remaining:

Step 3: Divide the initial quantity of radium by 2 for each half-life.
Initial quantity: 0.5 grams

1st half-life: 0.5 grams / 2 = 0.25 grams remaining
2nd half-life: 0.25 grams / 2 = 0.125 grams remaining
3rd half-life: 0.125 grams / 2 = 0.0625 grams remaining

Therefore, in 6836, the research hospital will have approximately 0.0625 grams of radium remaining.