The half-life of 145 over 59 Pr is 6.0 h. What fraction of an original sample of this radionuclide?

Question

would remain after 30.0 h has elapsed?

Answer 1

The information about the particular nucleotide is irrelevant and is probably there to confuse you! Since the half-lif eis 6 hours, after every 6 hours there is only half the amount that there was at the beginning of the 6 hour period. The proportion of the original sample that is there at the beginning is obviously 1. After 6 hours only half (1/2) remains. After the second six hours, only half of the 1/2 (i.e. 1/4) remains. After another 6 hours, 1/8 remains, then 1/16, and then 1/32. Specifically, after n half-life periods, 1/(2^n) remains.

This is, of course, a general result. The only thing you need to do is determine that 30 hours represents 5 half-life periods.

Answer 2

there are five of 6 hours in 30 hours
therefore left is (1/2)^5=1/32

Answer 3

5 half lives, so 1/2 x 1/2 ... 5 times = 1/32