5) Calculate each of the following involving half-lives: a. The half-life of Na-24 is 15 h. If the initial activity of
the sodium-24 is 6.4 mCi, what is its activity after 60. h. b. If a sample of 1-123 with an activity of 4 kBq decays
to an activity of I kBq in 26.4 h. what is its half-life?

Q5. (a.) Given : half-life of Na-24 = 15 h

time passed = 60 h

initial activity = 6.4 mCi

number of half-lives passed = (time passed) / (half-life)

number of half-lives passed = (60 h) / (15 h)

number of half-lives passed = 4

According to radioactive decay law,

final activity = (initial activity) / (2^a)

where

a = number of half-lives passed = 4

Substituting the values,

final activity = (6.4 mCi) / (2⁴)

final activity = (6.4 mCi) / (16)

final activity = 0.4 mCi

(b.) Given : initial activity = 4 kBq

final activity = 1 kBq

time passed = 26.4 h

According to radioactive decay law,

final activity = (initial activity) / (2^a)

where

a = number of half-lives passed

Substituting the values,

1 kBq = (4 kBq) / (2^a)

2^a = (4 kBq) / (1 kBq)

2^a = 4

2^a = 2²

a = 2

half-life = (time passed) / a

half-life = (26.4 h) / 2

half-life = 13.2 h