Question

A sample of radioactive 210X initially weighed 4.000 gram. After 35 days, 0.125 gram of this isotope remained,
the rest having decayed to the stable isotope 206Q.
(a) What is the half-life, in days of 210X?
(b) What mass, in grams, of 206Q is formed? (Assume that isotopic masses can be approximated using mass
numbers.)

Answer 1

(a)

Initial Mass = Q0 = 4.000 gms

After 35 days, Qt = 0.125 gms

For the first order reaction

ln(Q0/Qt) = kt

k = ln(2)/(t(half))

ln(4.000/0.125) = ln(2)/(t(half)) * 35

t(half) = 35 * ln(2)/ln(32) = 35/5 = 7 days

Hence the half life is equal to 7 days

(b)

Amount of 210X isotope decayed = Initial Mass - Final Mass = 35g - 7g = 28g

Mass of 206Q formed = Amount of 210X isotope * Molar mass of 206Q/Molar mass of 210X = 28 * 206/210 = 27.46 grams

Hence the mass of 206Q formed will be 27.46g