Q4. Radioactive elements decay via first-order kinetics. Consider a certain type of nucleus that has a rate constant of 2.4 × 10–2 h–1. A sample contains 6.5 × 108 radioactive nuclides. Calculate the time required for 59% of the nuclides to decompose.
a. 2.2 × 10–1 h
b. 2.2 × 101 h
c. 3.7 × 101 h
d. 1.0 × 101 h
e. 1.6× 101 h
ln(No/N) = kt
ln(100/59) = 0.024t
0.528 = 0.024t
t = 0.528/0.024 = 22 hr