How long will it take a sample of polonium-210 with a half-life of 140 days to decay to one-sixty-fourth of its original strength?

1/2 = e^k(140)

ln .5 = 140 k
k = .00495
so
1/64 = e^-.00495 t

-4.159 = -.00495 t
t = 840 days

alternatively

1/64 = (1/2)^6
so 6 half lives
=140*6 = 840 days

Well, let me grab my radioactive clown wig and crunch some numbers for you! If polonium-210 has a half-life of 140 days, it means that every 140 days, half of the atoms decay.

So, to decay to one-sixty-fourth of its original strength, we need to go through six half-lives, because 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/64.

Since each half-life is 140 days, multiplying that by 6 gives us a total of 840 days.

Therefore, it will take 840 days for the sample of polonium-210 to decay to one-sixty-fourth of its original strength. Just keep an eye out for any glowing clowns along the way!

To determine the time it takes for a sample of polonium-210 to decay to one-sixty-fourth (1/64) of its original strength, we can use the concept of half-life.

The half-life of polonium-210 is given as 140 days. This means that after every 140 days, the sample's strength will be reduced to half of its previous value.

To find out how many half-lives it takes for the sample to decay to 1/64 of its original strength, we need to calculate the number of times we can divide the original strength by 2 to reach 1/64.

1/64 is equivalent to (1/2)^6 since (1/2)^6 = 1/64.

Thus, it will take 6 half-lives for the sample to decay to 1/64 of its original strength.

Since each half-life is 140 days, we can multiply the number of half-lives by the half-life duration to find the total time:

6 half-lives * 140 days per half-life = 840 days.

Therefore, it will take a sample of polonium-210 with a half-life of 140 days approximately 840 days to decay to one-sixty-fourth of its original strength.

To determine how long it will take for the sample of polonium-210 to decay to one-sixty-fourth (1/64) of its original strength, we can use the concept of half-life.

First, let's understand what a half-life is. The half-life of a radioactive substance is the time it takes for half of the material to decay. In the case of polonium-210, its half-life is 140 days, meaning that after 140 days, half of the initial amount will have decayed.

Since we want to find out when the sample decays to 1/64th of its original strength, it means it needs to undergo six half-lives (2^6 = 64). Each half-life reduces the material to half of its previous strength.

Now, let's calculate the time it takes for the sample to decay to 1/64th of its original strength:

1st half-life: After 140 days, the sample will be 1/2 of its original strength.
2nd half-life: After another 140 days (2 * 140 = 280 days in total), the sample will be 1/4 of its original strength.
3rd half-life: After another 140 days (3 * 140 = 420 days in total), the sample will be 1/8 of its original strength.
4th half-life: After another 140 days (4 * 140 = 560 days in total), the sample will be 1/16 of its original strength.
5th half-life: After another 140 days (5 * 140 = 700 days in total), the sample will be 1/32 of its original strength.
6th half-life: After another 140 days (6 * 140 = 840 days in total), the sample will be 1/64 of its original strength.

Therefore, it will take 840 days for the sample of polonium-210 to decay to one-sixty-fourth of its original strength.