Question

Radioactive iodine is used frequently in biological studies. A radiation biologist studies the rate of decomposition of this substance and obtains the following data:

t (days)....... 0 ...........4.0 ..........8.0 ..........12.0 ...........16.0

Mass (µg) 12.0........ 8.48.......... 6.0 ...........4.24 ...........3.0

(a) Assume this is a first order reaction, determine the rate constant, including appropriate units. (b) How many micrograms will be left after 32 days? (c) How many days will it take for the sample size to decrease to 1.2 µg?

Answer 1

Apply Half life equation

A = A0*(1/2)^(t/HL)

A0 = 12 micrograms

1/2 of A0 = 12/2 = 6 micrograms, when this happens, t = 8 days

this must be the half life so

HL = 8 days

then

a)

for a first order equation, the half life is given as:

t1/2 = ln(2)/k

solve for k

k = ln(2)/(8) =  0.08664 1/day

b)

after t = 32, find mass

A = (A0)(1/2)^(t/HL)

A = (12)(1/2)^(32/8) = 0.75 micrograms left after 32 days

c)

time require dfor A final = 1.2 micrograms

A = (A0)(1/2)^(t/HL)

1.2 = 12*(1/2)^(t/8)

solve for t

0.1 = (0.5)^(t/8)

t = 26.57 days