# maths: differencial ย equations?

The rate at which a radioactive specimen decays is given by

d๐/d๐ก=โ๐ผ๐

where ๐ is the number of radioactive particles at time ๐ก and ๐ผ is a constant. Solve this equation to find an expression for ๐ as a function of time given that ๐=๐0 at ๐ก=0. Hence find the half-life of the specimen i.e. the time taken for the number of radioactive particles to halve.

### 2 Answers

Relevance

- az_lenderLv 73 weeks ago
dN/N = -alpha dt =>

N = c e^(-alpha t),

and N(0) = No implies

N = No * e^(-alpha t).

The half-life is the time when

1/2 = e^(-alpha t), or

ln(2) = alpha t, or

t = [ln(2)]/alpha.

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