Half-life of silicon if 50 grams are present how many in 500 years

Question

the half-life of silicon-32 is 710 years. if 50 grams are present now how much will be present in 500 years?

Answer 1

Sample decay can be predicted using the formula

m(t) = m₀ e^-rt,

where m₀ is the starting mass (here, 50 g), and r is related to how quickly the sample decays. For half-lives, we know that half of the mass will be left after the half-life time has elapsed, so that

1/2 = e^-rt',

where t' indicates the half-life time (here, 500 years). Solving using algebra for r, we find

ln(1/2) = ln(e^-rt')

-ln(2) = -rt'

r=ln(2)/t'

r=ln(2)/710

r=0.000976

Now that we have the rate constant, we can plug back into the original formula to find the mass after 500 years, namely

m(t = 500 yrs) = 50 e^{-(0.000976)(500)}

^{m(500 yrs) = 30.069 g}

^{I'm not sure how you will want to round the significant figures. If there is only one or two, then the mass may be reported as m(500 yrs) = 30 g.}

Answer 2

Use formula,

N = N₀ e ^(-0693t/T)

Given N₀ = 50 gm , T = 710 years , t= 500 years

N = 50/ e ^{( 0.693*500 /710)} = 50/ / e ^0.488 = 50/ 1.629

N= 30.693 gm