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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