Problem P. 5270. (November 2020)

P. 5270. The half life of the isotope radon-222 is 5508 minutes. How many days elapses until the activity of the radon sample decreases to one-tenth of its original value?

(4 pont)

Deadline expired on December 15, 2020.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. Az aktivitás időbeli változása:

\(\displaystyle A(t)=A(0)\, 2^ {-t/T_{1/2}}.\)

\(\displaystyle A(t)=\tfrac1{10}\,A(0)\) akkor teljesül, ha

\(\displaystyle 2^{-t/T_{1/2}}=0{,}1\qquad \text{tehát}\qquad -\frac{t}{T_{1/2}}\cdot \lg 2=-1,\)

azaz

\(\displaystyle t=\frac{1}{0{,}3}\cdot 5508~\text{perc}=12{,}7~\text{nap}.\)

A preparátum aktivitása tehát kb. 13 nap alatt csökken az egytizedére.

Statistics:

91 students sent a solution.
4 points:	67 students.
3 points:	13 students.
2 points:	4 students.
1 point:	4 students.
0 point:	3 students.

Problems in Physics of KöMaL, November 2020