Answer to Question #170936 in General Chemistry for koo

Question

Co-60 is used extensively in radiotherapy as a source of y-rays. Its half-life is 5.27 years. a) How many years will it take to decrease to 35% of its original activity? b) If a cobalt source is ten years old, what percent of its original activity remains?

Answer 1

a) $\lambda$ = 1/t_1/2 = 1/5.27 y^-1

t =( 1/$\lambda$ ) ln $\frac{N_o}{N_t}$

decrease to 35% of N_o

t = 5.27 × ln $\frac{N_o}{0.35N_o}$

t = 5.27× ln( 2.857)

t = 5.27×1.04972

t = 6.004 years

b) N_t = N_o × e^{(--1/5.27)×10}

N_t = N_o × e^-1.89

N_t = 0.15N_o

15%