Home > Chemistry > Nuclear Half-Life Calculations

An original sample of K-40 has a mass of 25.00 grams. After #3.9 xx 10^9# years, 3.125 grams of the original sample remains unchanged. What is the half-life of K-40?

Answer 1

Henry Antrim

#1.3xx10^9 yrs#

From #C_"final" = C_"initial"e^(-kt)# solve for rate constant (k) ...

=> #k = (ln(C_f/C_i)/-t)# = #ln(3.125/25)/(-3.9xx10^9)# = #5.33xx10^-10 yrs^-1#

In the half-life equation, use the rate constant (k).

=> #t_(1/2) = (0.693/k) = (0.693/(5.33xx10^-10))years# #1.3xx10^9 years#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Mateo Aguilar

The half-life of K-40 is approximately 1.25 billion years.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.