# Half-Life Formula

It is the time requires to decay in half. Half-life is the time required for the amount of something to fall to half its initial value. The mathematical representation of Half life is given by,

(Half life time) = (Napierian logarithm of 2)/(disintegration constant)

The equation is:

t_{1/2} = ln(2)/λ

Where:

λ : disintegration constant of the system

t_{1/2}: Half life time

Half-life Formula Questions:

1) What is the half life of a radioactive substance whose disintegration constant is 0.005 years^{(-1)}?

Answer:

Substituting the data in the half-life formula

t_{1/2} = ln(2)/(0.005 years^{(1)})

t_{1/2} = ln(2)*200 years

t_{1/2} = 138.62 years

2) What is the disintegration constant of a process whose half life time is 10 minutes?

Answer:

From the half-life formula we find the disintegration constant

λ = ln(2)/t_{1/2}

λ = ln(2)/(600 s)

λ = 0.00115 s^{(-1)}

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