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Calcolatore di Half-Life

Calcolo dell'emivita e della quantità di una sostanza passo dopo passo

Questa calcolatrice calcola il tempo di dimezzamento, la quantità iniziale, la quantità rimasta e il tempo, con i passaggi indicati.

There are units of mass of a substance with a half-life of units of time. In units of time, there will remain units of mass of the substance.

Enter any three values.

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Solution

Your input: find N(t) in N(t)=N0eλt given N0=250, th=15, t=100.

N(t) is the amount after the time t, N0 is the initial amount, th is the half-life.

First, find the constant λ (also known as decay constant or decay rate).

We know that after half-life there will be twice less the initial quantity: N(th)=N02=N0eλth.

Simplifying gives 12=eλth or λ=ln(12)th.

Plugging this into the initial equation, we obtain that N(t)=N0eln(12)tht or N(t)=N0(12)tth.

Finally, just plug in the given values and find the unknown one.

From N(t)=250(12)10015, we have that N(t)=1253264.

Answer: N(t)=12532642.46078330057592.