Question

The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 35 seconds? A=A0ekt

Answer 1

Answer:

1.415 gram of the element will be left.

Step-by-step explanation:

The decay of radioactive element Krypton-91 can be formulated as  

$A_{t} = A_{0} e^{-kt}$ ............ (1)

where, $A_{0}$ is the initial amount of the element.

$A_{t}$ is the amount of element left after t seconds.

And k is a rate constant.

Now, given that the half-life of the element is 10 seconds.

So, from equation (1) we get

$0.5 = e^{- k \times 10}$

taking ln on both sides, we get.

ln 0.5 = -10k

⇒ k = 0.0693

So, the equation (1) becomes $A_{t} = A_{0} e^{-0.0693t}$ ........ (2)

Now, if 16 gram of the element are initially present, then we asked to determine the amount of the element left after 35 seconds.

So, from equation (2) we have $A_{t} = 16 e^{- 0.0693 \times 35} = 1.415$ gm.

So, 1.415 gram of the element will be left. (Answer)