### Chemistry Formulas

# Rate of Decay Formula – Equation and Problem Solved with Example

This is not possible to predict the decay of a nucleus and it is not even affected by the physical factors like temperature, pressure etc. the rate of decay majorly depends on two factors – the total number of nuclei that are not decayed yet and the total number of nuclei available in the system.

Few isotopes decay rapidly and some of them will take time. With the help of rate of decay, you can always calculate the number of nuclei that decay per second. Let us see how rate of decay formula could be given –

### N_{t} = N_{0} e^{-λt}

N_{t} = the amount of radioactive particles are time (t)

N_{0} = the amount of radioactive particles at time = 0

λ = rate of decay constant

t = time

In simple words, decay presents how quickly something will die or disappear. Decay is usually measured to quantify the exponential decrease in the nuclear waste. Obviously, you should have a clear idea of the initial population and the final population.

One other term is exponential decay when amount of decrease is directly proportional to the total amount that exists. So, how to calculate the rate of decay in Chemistry. You should divide the final count by the initial count to find the decayed value.

You can also find the value with the help of calculator as well but a depth understanding of the concept will always help you in solving tough problems too. If the value is negative then It clearly indicates a decay at a particular time period. However, the rate of decay depends from nuclei to nuclei. The number of undecayed nuclei will simply double the rate of decay.