Question

Radioactive decay can be described by the following equation In A = In A_0 -kt Where A_0 is the original amount of the substance, A is the amount of the substance remaining after time t, and k is a constant that is characteristic of the substance. For the radioactive isotope lead -214, k is 2.59 times 10^-2 minutes^-1 If the original amount of lead - 214 in a sample is 25.9 mg, how much lead-214 remains after 29.7 minutes have passed?

Answer 1

Answer: The amount of lead-214 remaining after given time is 12 mg.

Step-by-step explanation:

The equation used to calculate the amount of sample for first order kinetics follows:

`\ln A=\ln A_o-kt`

where,

`A_o` = initial mass of isotope = 25.9 mg

N = mass of the isotope left after the time = ? mg

t = time = 29.7 min

k = rate constant =
`2.59* 10^(-2)min^(-1)`

Putting values in above equation, we get:

`\ln A=\ln (25.9mg)-(2.59* 10^(-2)min^(-1)* 29.7min)\\\\A=12mg`

Hence, the amount of lead-214 remaining after given time is 12 mg.