A specimen taken from the wrappings of a mummy contains 7.02 g of carbon and has an activity of 1.34 Bq. How old is the mummy? Determine its age in years assuming that in living trees the ratio of 14C/12C atoms is 1.23E-12

I am not able to get the answer.Please help

Do you have an answer?

Yes. But it is incorrect

R = 1.34 Bq = 1.34 decays / second Mass of sample = 7.02 g

For 14 C T 1/2 = 5700 years (approximate value)

= 5700 x 365 x 24 x 60 x 60 =1.8 x 10 11 seconds

T 1/2 = 0.6931 / λ

λ = 0.6931 / 1.8 x 10 11 = 3.86 x 10 -12 per second

Number of atoms contained in 7.02 g of carbon (12 C atoms)

= (7.02 x 6.023 x 10 23) /14 = 3.02 x 10 23

14 C atoms / 12 C atoms = 1.23 x 10-12

No of 14 C atoms (radioactive) = No of 12 C atoms x 1.23 x 10-12

N0 = 3.02 x 10 23 x 1.23 x 10-12 = 3.7146 x 10 11

R = Nλ

N = R/λ = 1.34 / 3.86 x 10 -12 = 3.4715 x 10 11

t = 3.323 x 5700 x In (3.4715 x 10 11 / 3.7146 x 10 11 ) = 557 years

To determine the age of the mummy, we need to use the concept of carbon dating. Carbon dating relies on the fact that a small percentage of carbon atoms in the atmosphere is radioactive carbon-14 (14C), which is incorporated into living organisms. When an organism dies, it no longer takes in new carbon-14, and the existing carbon-14 begins to decay.

To find the age of the mummy, we can use the equation:

N(t) = N0 * e^(-λt)

where
- N(t) is the remaining amount of 14C atoms after time (t)
- N0 is the initial amount of 14C atoms (carbon content) in the specimen
- λ (lambda) is the decay constant for carbon-14 (approximately 1.21 x 10^(-4) year^(-1))
- t is the time in years

First, we need to determine the initial amount of 14C atoms (N0) in the specimen. We know that the carbon content of the specimen is 7.02 g, but we need to convert this to the number of atoms. The atomic mass of carbon is approximately 12 g/mol.

Number of moles of carbon = mass of carbon / atomic mass of carbon
Number of moles of carbon = 7.02 g / 12 g/mol

Next, we need to find the number of 14C atoms by multiplying the number of moles of carbon by Avogadro's number (approximately 6.022 x 10^23 atoms/mol).

Number of 14C atoms = number of moles of carbon * Avogadro's number

Now that we know the initial amount of 14C atoms, we can solve for the age (t) using the given activity (1.34 Bq) and the ratio of 14C/12C atoms (1.23 x 10^(-12)), which is the radioactive decay constant λ.

N(t) = N0 * e^(-λt)
Activity (A) = λ * N(t) [Activity is the decay constant multiplied by the number of atoms remaining]

Solving for time (t):

t = -ln(A / (λ * N0)) / λ

Substituting the given values:

t = -ln(1.34 Bq / (1.21 x 10^(-4) year^(-1) * N0)) / (1.21 x 10^(-4) year^(-1))

Now that we have the value of t, we can calculate the age of the mummy.

Note: This calculation assumes that the ratio of 14C/12C atoms in living trees is the same as the ratio in the specimen from the mummy.