The practical limit to ages that can be determined by radiocarbon dating is about 41000-yr-old sample, what percentage of the original 614c atoms remains? (for percentage you can either enter the percentage with a percent sign "65.1%" or the percentage as a fraction "0.651".)

In percentage, the sample of C-4 remains = 0.7015 %

Explanation:

The Half life  Carbon 14 =  5730 year

Where, k is rate constant

So,  

The rate constant, k = 0.000120968 year⁻¹

Time = 41000 years

Using integrated rate law for first order kinetics as:

Where,  

is the concentration at time t

is the initial concentration

So,  

In percentage, the sample of C-4 remains = 0.7015 %

put the answers   and i could answer.

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml