Suppose you have 100 g of radioactive plutonium-239 with a half-life of 24,000 years. How many grams will remain after (a) 12,000 years (b) 24,000 years (c) 96,000 years?
after 24000 yrs 50g will be left.......after 96000 yrz grams left will be 12.5 grams.....and they not decay after 12000 yrs since half life is 24000 yrs not 12000 yrs
To calculate the amount of plutonium-239 remaining after a certain period of time, we can use the formula:
Amount remaining = Initial amount × (1/2)^(time elapsed / half-life)
In this case, we have an initial amount of 100 g and a half-life of 24,000 years. Let's calculate the amount remaining after each time period:
(a) After 12,000 years:
Amount remaining = 100 g × (1/2)^(12,000 / 24,000) = 100 g × (1/2)^0.5 = 100 g × 0.707106 = 70.71 g (rounded to two decimal places)
(b) After 24,000 years:
Amount remaining = 100 g × (1/2)^(24,000 / 24,000) = 100 g × (1/2)^1 = 100 g × 0.5 = 50 g
(c) After 96,000 years:
Amount remaining = 100 g × (1/2)^(96,000 / 24,000) = 100 g × (1/2)^4 = 100 g × 0.0625 = 6.25 g
Thus, after (a) 12,000 years, (b) 24,000 years, and (c) 96,000 years, the remaining amounts of plutonium-239 would be approximately (a) 70.71 g, (b) 50 g, (c) 6.25 g, respectively.