Question

Because the slopes of your plots are the negative of the decay constant, you can use the equation derived in Part 1 to calculate the half life of hydrogen-3 and carbon-14. Show your work for the calculation below.

The number of radioactive particles is governed by the equation: N(t)= N0e−λt where N(t) is the number of radioactive particles after time t, ^N0 is the original number of particles, and λ is the decay constant. Show that the half life (the time it takes for half of the original number of particles to decay) of a radioactive isotope, ^t1/2 , is given by the equation:

0.693

t1/2 =   

N (t)

Hint: the ratio of ^N0 is ½ when ^t=t1/2 .

- N(t) = Noe^ –(lambda)t

- N(t)/No = Noe^-(lambda)t

- N(t)/No = e^-(lambda)t

- N(t) = 50%, No = 100%

- 50/100= e^-(lambda)t

- 0.5 = e^-(lambda)t

- ln(0.5)= -(lambda)t

- 0.693 = -(lambda)t

- -0.693/-lambda

- t1/2 = 0.693/lambda

So i'm supposed to calculate the half life for Hydrogen-3 and Carbon-14 using what i had done above and I can't figure out which formula to use and what values go where.

Answer 1

I hope this will help you in determining the half life.