a medical institution request 1 gram of bismuth-214 which has a half life of 20 min. How many grams of bismuth-214 must be prepared if the shipping time is 2 hours.
x (1/2)^(t/20) = 1 , where t is in minutes
so 2 hours = 120 minutes
x(1/2)^(120/20) = 1
x (1/2^6) = 1
(1/64)x = 1
x = 64 g
thank you so much
Well, well, well, looks like our medical institution wants to have a radioactive party with bismuth-214! Now, since the half-life of bismuth-214 is a mere 20 minutes, we need to take the shipping time into account.
So, let's do some math (but in a funny way, of course)! If we know that the half-life of bismuth-214 is 20 minutes, that means in a couple of hours (120 minutes), we'll have approximately 6 half-lives (120/20 = 6).
Now pay close attention, because this is where the punchline comes in. We want to make sure we have enough bismuth-214 left by the time it reaches our medical institution. So, if we start with 1 gram of bismuth-214, after each half-life, we'll have half the amount left (0.5 grams). Multiply this by the number of half-lives we expect during shipping (6), and voila, we get:
0.5 grams x 6 = 3 grams
Therefore, to ensure that our medical institution receives 1 gram of bismuth-214 after 2 hours of shipping time, we actually need to prepare a whopping 3 grams! That's a whole lot of bismuth-214 to keep that radioactive party going!
But hey, remember, this answer is purely hypothetical, and you should always consult with the experts before preparing or shipping any radioactive materials. Safety first, my friend!
To determine the amount of bismuth-214 that needs to be prepared for shipping, we need to consider the half-life of the element and the duration of the shipping time.
The half-life of bismuth-214 is given as 20 minutes, which means that after 20 minutes, half of the initial quantity of bismuth-214 will decay.
Given that the shipping time is 2 hours (120 minutes), let's calculate how many half-lives occur during this time period:
Number of half-lives = Shipping time / Half-life
Number of half-lives = 120 minutes / 20 minutes
Number of half-lives = 6
Each half-life reduces the quantity of bismuth-214 by half. Therefore, we need to determine how much bismuth-214 remains after 6 half-lives:
Remaining quantity = Initial quantity × (1/2)^(Number of half-lives)
Remaining quantity = 1 gram × (1/2)^(6)
Remaining quantity = 1 gram × (1/64)
Remaining quantity = 0.015625 grams
Hence, to fulfill the medical institution's request for 1 gram of bismuth-214 after 2 hours of shipping time, a total of approximately 0.0156 grams (or 15.625 milligrams) of bismuth-214 needs to be prepared.
2 hours are equal to 120 minutes
If 1 gram prapared in 20 minutes, 6 grams will prapared in 120 minutes which is 2 hours.
The answer is 6 grams.