Answer:
A general equation is given below; it takes two t1/2 to decay 10% of the material.
Explanation:
Decay constant, k = [tex]\frac{ln 2}{t_{1/2} }[/tex]
But [tex]ln (\frac{N_{t} }{N_{o} })[/tex] = -kt
Where Nf = final amount
No = initial amount
t = time elapsed
a.)
Initially, 5% of 100mg has decayed:
ln [tex]\frac{95}{100}[/tex] = -k × 2 years
k = -0.051293 ÷ (-2)
=0.0256
⇒ The equation for mass at any time t for this material, Nt :
[tex]N_{t} = 95. e^{-0.0256t}[/tex]
b.)
at 10% decay of 100mg,
Nt = 90mg
⇒ [tex]ln (\frac{90}{100})[/tex] = -0.0256 × t
∴ t = 4.108 ≅ 4.1 years (or 2 half lives)
