A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there are 100 milligrams of the material present and if after two years it is observed that 5 percent of the original mass has decayed, find (a) an expression for the mass at any time t and (b) the time necessary for 10 percent of the original mass to have decayed.

A general equation is given below; it takes two t1/2 to decay 10% of the material.

Explanation:

Decay constant, k =

But = -kt

Where Nf = final amount

No = initial amount

t = time elapsed

a.)

Initially, 5% of 100mg has decayed:

ln = -k × 2 years

k = -0.051293 ÷ (-2)

=0.0256

⇒ The equation for mass at any time t for this material, Nt :

b.)

at 10% decay of 100mg,

Nt = 90mg

⇒ = -0.0256 × t

∴ t = 4.108 ≅ 4.1 years (or 2 half lives)

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