Consider a 1.0 g sample of carbon with 14C / 12C of 1.3 x 10-12. How many atoms

Question

Consider a 1.0 g sample of carbon with 14C / 12C of 1.3 x 10-12. How many atoms does it contain? How many 14C atoms does it contain? What is the activity of the sample? Draw a graph of the number of 14C atoms with time. On your graph, mark the half-life and the time constant. Draw a graph of the activity of the sample with time. On your graph, mark the half-life and the time constant. Calculate how long it will take for the sample to have a 14C / 12C of 1.3 x 10-10 . Does this agree with your graph? Calculate how long it will take for the activity of the sample to decrease to 1.0 % of its original value. Does this agree with your graph?

Explanation / Answer

let the amount of 12C is x

then the amount of 14C = 1.3*10^(-12)*x

now 14*1.3*10^(-12)*x+12*x = 1/1.6726*10^(-24) mass equation.

solving we get x = 5*10^22

so the total atm of carbon = 5*10^22 + 6.5*10^10

the total number of 14C atom = 6.5*10^10.

knowing the conc of the 14C we can easily find the activity by using the formulae = (conc)*e^(-lamda*t)

for calculating the second last part u can easily find it by using the above formulae .

taking conc to the given conc of 14C = 6.5*10^10 and using the lamda given we can easily find the time at which the cocentration will be as required.

all question need the value of lamda and the required formula i have written to find the concentration of the 14C at any time .

similarly the graph will be a decaying exponential.

with its y intercept at the conc found in the first question.

where the cocn become half that will be the life time which can easily be found by using the formulae

=> (6.5*10^10)*e^*(-lamda*t)= (6.5*10^10)/2

using the given lamda u can calculate the time.

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