Question

1. Iodine-131 is an isotope in the treatment of hyperthyrodisim and has an effective half- life of 7.6 days. If a patjent is given a dose of 10.0 mCi, how much radiation remains after 38 days?

2. Phosphorus-32 is a radisotope used to detect certain types of tumors. P-32 has an effective half-life of 14.1 days. If a patient recieves 6.0 mCi, how much radiatjon remains after 169.2 hours?

Answer 1

We have, decay constant ( ) = 0.693 / t _1/2

Where, t _1/2 is a half-life radioactive element.

Decay constant of I - 131 =  = 0.693 / t _1/2 = (0.693 / 7.6 days ) = 0.09118  days^-1

We have equation: t =2.303 /    log (N ₀ / N _t)

Where, is a decay constant

N ₀ is the initial amount of radioactive element,

N _t is the amount of radioactive element after time t.

In this example, N ₀ = [I - 131] ₀ = 10.0 mCi

N _t = [I - 131] _t =?

t =38 days

Hence, 38 days = 2.303 / 0.09118  days^-1 log 10.0 mCi / [I - 131] _t

log 10.0 mCi / [I - 131] _t = 38 days x 0.09118  days^-1 / 2.303 = 1.5045

log 10.0 - log [I - 131] _t  = 1.5045

1.0 - log [I - 131] _t  = 1.5045

log [I - 131] _t  =1.0 -1.5045 =- 0.5045

[I - 131] _t  =10 ^{- 0.5045} = 0.3130 mCi

ANSWER: Radiation remained in patient body after 38 days is 0.3130 mCi

PART 2

We have, decay constant ( ) = 0.693 / t _1/2

Where, t _1/2 is a half-life radioactive element.

Decay constant of P -32 =  = 0.693 / t _1/2 = (0.693 / 14.1 days ) x ( 1 day / 24 hour ) = 2.048 x 10 ^-03 hr^-1

We have equation: t =2.303 /    log (N ₀ / N _t)

Where, is a decay constant

N ₀ is the initial amount of radioactive element,

N _t is the amount of radioactive element after time t.

In this example, N ₀ = [P-32] ₀ =6.0 mCi

N _t = [P-32] _t =?

t =169.2 hr

Hence, 169.2 hr = 2.303 / 2.048 x 10 ^-03 hr^-1 log 6.0 mCi / [P-32] _t

log 6.0 mCi / [P-32] _t =169.2 hr x 2.048 x 10 ^-03 hr^-1 / 2.303 = 0.1504

log 6.0 - log  [P-32] _t = 0.1504

0.7782 - log  [P-32] _t = 0.1504

log  [P-32] _t = 0.7782 - 0.1504 = 0.6278

[P-32] _t = 10 ^0.6278 = 4.244 mCi

ANSWER: Radiation remained in patient body after 169.2 hrs is 4.244 mCi