An isotope of radon gas, Rn-222, undergoes decay with a half-life of 3.8 days. How long does it take for the amount of Rn-222 to be decreased to one-sixteenth of the original amount?

Wrong, it takes 15.2 days

To determine how long it takes for the amount of Rn-222 to decrease to one-sixteenth (1/16) of the original amount, we need to use the concept of half-life.

A half-life is the time it takes for half of the radioactive substance to decay. In this case, the half-life of Rn-222 is 3.8 days, meaning that every 3.8 days, half of the Rn-222 atoms will decay.

Since we're interested in finding the time it takes for the amount to decrease to 1/16 of the original amount, we need to find out how many half-lives it would take to achieve that.

1/16 is equivalent to (1/2)^4. In other words, it takes four half-lives for a substance to decrease to 1/16 of the original amount.

So, to find the time it takes for the amount of Rn-222 to decrease to 1/16, we multiply the half-life by the number of half-lives it takes: 3.8 days * 4 half-lives = 15.2 days.

Therefore, it takes approximately 15.2 days for the amount of Rn-222 to be decreased to one-sixteenth of the original amount.

well, 1/16 = 1/2^4

so it takes 4 half-lives