Question

Be sure to answer all parts of the question:

a. A fabric remnant from a burial site has a ¹⁴C/¹²C ratio of 0.655 of the original value. How old is the fabric?
____ yr

b. If 5.01 × 10⁻⁹ mol of ¹⁷⁶W emits 1.07 × 10¹⁵ β⁺ in 1.00 h, what is the decay constant? Enter your answer in scientific notation.
____ × 10___ h⁻¹

Answer 1

(a) The change in the amount of 14C(N) IS given

d(N)/d(t) = -λ*N where λ is decay constant

integration of above equation -

∫dN/N = -λ∫dt ; N = N₀e^-λt.........(1)

Half life of carbon is 5730 years

it means at t = t_1/2 ; N = N₀/2 ; Putting these value in equation (1)

N₀/2 =N₀e^-λt  
λ = ln(2) / t_1/2 = 0.693/5730=1.21x10^-4 yr^-1

Given N/N₀ = 0.655 Using value of N/N₀ and λ in (1)   

N/N₀ = e^-λt

ln(N₀/N) = λt ......(2)

t = ln(1/0.655)/1.21x10^-4 yr^-1    =3496yr

So the fabric is 3496yrs old

(b) N = N₀e^-λt

Initially no of particle ( N₀)= mole*N_A   =5.01 × 10⁻⁹*6.023*10²³ = 3*10¹⁵

Given N(particles(β⁺) at any time ) = 3*10¹⁵-1.07 × 10¹⁵= 2*10¹⁵

Time(t) = 1hr

By equation (2)

ln(3*10¹⁵/2 × 10¹⁵) = λ*1hr ; λ = 0.405hr^-1

The decay constant( λ ) =4.05*10^-1hr^-1