Question

Radioactive decay can be described by the following equation In A = In Ao- kt where Ao 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. minutes For the radioactive isotope chromium-56, k is 1.17 x 10 If the original amount of chromium-56 in a sample is 34.5 mg, how much time is needed for the amount of chromium- 56 that remains to fall to 20.3 mg?

Answer 1

Answer: The amount of time needed is 4.53 minutes.

Step-by-step explanation:

The equation used to calculate time period follows:

`\ln A=\ln A_o-kt`

where,

`A_o` = initial mass of Cr-56 isotope = 34.5 mg

A = mass of the Cr-56 isotope left after the time = 20.3 mg

t = time = ? min

k = rate constant =
`1.17* 10^(-1)min^(-1)`

Putting values in above equation, we get:

`\ln (20.3)=\ln (34.5)-[(1.17* 10^(-1)min^(-1))* t]}\\\\t=(\ln(34.5)-\ln(20.3))/(1.17* 10^(-1))=4.53min`

Hence, the amount of time needed is 4.53 minutes.