Answer to Question #135595 in General Chemistry for Joe

Question

the half-life of radon-222 is 3.824 day. when you are 97 years old, you come across a 60 atom sample of Radon-222. After what time (in days) will 15 atoms of the original sample remain?

Answer 1

Given,

the half-life of radon-222, (t)1/2 = 3.824 day

There are a 60 atom in sample of Radon-222.

We know that half life of radioactive sample, (t)1/2 = ln2/k

Where k = decay constant of the radioactive element.

Putting the values given,

3.824 = ln2/k

Or, k = ln2/3.824

Or, k ≈ 0.1813 /day

According to the integrated decay equation,

ln(N°/N) = kt_____[A]

where, N° = number of radioactive atoms present in the sample at the beginning.

N = number of radioactive atoms present in the sample at the time = t

Putting the values in the above equation [A] we get.

ln(60/15) = 0.1813 × t

Or, ln4 = 0.1813 × t

Or, t = ln4/0.1813

Or, t = 7.646 (up to three significant decimal)

Hence after 7.646 days 15 atoms of radon-222 to remain in the sample