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That is completely unrealistic. C-14 has a half-life of several thousand years, not a few hours as implied in this example.

Anyway, to solve this in general you can write the exponential equation:

N = N0e-λt

where N is the remaining amount, N0 is the original amount, λ is the decay constant, and t is the time. Replace the numbers you know, and solve for λ. Note that the "disintegrations per minute" are proportional to the amount of remaining substance, so you can just as well assume that those numbers represent the remaining amount.

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Q: What is the decay constant for an isotope of carbon14 that has an activity of 6103 disintegrations per minute when first measured and 4103 disintegrations per minute four hours later mol wt14gmol?
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