How long will it take for the 100mg of cesium-137 to decay to 6.25mg(1/16 the original amount)?

2n = 16

Solve for n = number of half lives.

still i can't understand it

Do you have the half-life given in the problem or are you allowed to look it up? If so there is an easier way to set it up.

To solve 2n = 16, take the log of both sides.
log 2n = log 16
n*log 2 = log 16
n*0.301 = 1.2 etc.

There is another way. Remember that half-life means the time it takes for 1/2 the material to disappear. So make a table like this. The periods are used for spacing.
amount......# half-lives
100 mg.........0
50 mg..........1
25 mg..........2
12.5 mg........3
6.25 mg........4
So whatever the half-life is, multiply that by 4 and you will have the time it takes to go through 4 half-lives.

thanks alot , this answer really helped me to understand this question

To determine the time it takes for the 100mg of cesium-137 to decay to 6.25mg, you need to calculate the decay time using the concept of half-life. The half-life of cesium-137 is approximately 30.17 years.

Here's how you can calculate the time:

1. Start by finding the number of half-lives that need to occur to reach 6.25mg. Since 6.25mg is 1/16th of the original amount (100mg), it means 4 half-lives have passed. This is because each half-life reduces the initial amount of cesium-137 by half.

2. Next, multiply the half-life by the number of half-lives to get the total decay time. In this case, since each half-life is 30.17 years, multiply it by 4 to get a total decay time of 120.68 years.

Therefore, it will take approximately 120.68 years for 100mg of cesium-137 to decay to 6.25mg.