Rutherfordium- 265 is a radioactive substance that has a half-life of 13 hours. if there is a 149g sample of rutherfordium- 265 left at 12am on october 19th, approximately how much rutherfordium- 265 would remain on october 22nd at 12am?

3.21 grams

Step-by-step explanation:

First we are finding the radioactive decay constant using the formula:

lambda =

where

lambda is the radioactive decay constant.

is the half life of the radioactive substance.

We know from our problem that Rutherfordium- 265 has a half-life of 13 hours, so let's replace the value in our formula.

lambda =

lambda = 0.0533 per hour

Now we can use the decay formula to find the remaining quantity of the substance:

where

is the ending amount

is the beginning amount

is the time (in hours)

We know from our problem that there is a 149g sample of Rutherfordium- 265 left at 12am on October 19th, so . Notice that there are exactly 3 days from 12 am October 19th to 12 am October 22nd, so we have ; therefore . Now we can replace all the values in our formula:

We can conclude that 3.21 grams of Rutherfordium- 265 would remain on October 22nd at 12 am.

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898.1666667

step-by-step explanation:

5389/6 = 898.1666667