the half life radium-222 is 4 days. if a sample of radon-222 undergoes decay for 12 days, how much of the original parent isotope will be left?
You've made a typo. Do you mean Radium or Radon? I'll assume Rn-222.
k = 0.693/t1/2
Then ln(No/N) = kt.
Substitute and solve for N
To determine how much of the original parent isotope radium-222 will be left after 12 days, we need to use the concept of half-life.
The half-life of radium-222 is 4 days, which means that every 4 days, half of the original amount of radium-222 will decay.
To calculate how many half-lives have passed after 12 days, we divide the total time by the half-life:
Number of half-lives = Total time / Half-life
Number of half-lives = 12 days / 4 days = 3 half-lives
After 3 half-lives, half of the original amount of radium-222 will decay each time. So, after 3 half-lives, the remaining amount will be:
Remaining amount = (1/2)^(number of half-lives) × Initial amount
Remaining amount = (1/2)^3 × Initial amount
Remaining amount = (1/8) × Initial amount
Therefore, after 12 days, only 1/8 or 12.5% of the original parent isotope radium-222 will be left.