Radioactivity, Activity and Half-Life Calculation 

The activity is calculated by multiplying the number of mercury atoms in the sample by the decay constant for mercury. The number of atoms can be calculated if you know the mass of the sample. Divide the mass in grams by the number of grams per mole (200.59) for mercury. Multiply this result by Aavagadro's Number. The decay constant is found by dividing 0.693 by the half-life of the particular isotope of mercury (which you did not specify). Use Google to find the half-life after you find the isotope for your situation.

Yes, the Becquerel is the SI unit for activity for a radioactive substance, and, as you say, if one radioactive nucleus decays in one second the activity value is 1 Bq.

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No, N must be the number of radioactive nuclei. (1 nucleus per atom). Convert the number of grams to the number of nuclei following the example calculation in the video.

The activity is calculated by multiplying the number of atoms (nuclei) of Sr90 by the decay constant value. With your units the activity would have units of decays per second. If the decay constant you listed is a given value you should use that value. I would caution you that the actual decay constant for Sr909 is closer to 7.6 x 10^-10 (1/sec) than the value you listed.

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This RU-vid video should help you work out the answer to your problem. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-SmewSXd_pCk.html The key concept needed to solve this problem is tat the activity decreases exponentially.

View this RU-vid video. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-SmewSXd_pCk.html

This video uses a given half-life value to calculate other quantities. This video does not calculate the half-life value. Sorry if the title misled you.

No, the exponent is +7...31.56 million seconds in a year.

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I would suggest you perform the calculation for lamda with the known data first. e.g. lamda = activity / N Then calculate the half life = 0.693 / lamda. Next, change the activity number by, say 2%, and recalculate the half life. Then change the value of N by, say 2%, and recalculate the half-life. Now you will have an indication of how the half-life number changes for a 2% change in the activity and N values.

And was is the activity of mercury

And where did 90g/mole come from?

Yes The decay constant, lamda, is equal to .693 divided by the half life. Also note that Euler's number, e, raised to the power of .693 is equal to 2

This isotope has an atomic mass number of 90. The atomic mass number can be used to give an approximate value for the number of grams per mole.