Question

The technetium isotope 99Tc is useful in medical imaging, but its short 6.0 h half-life means that shipping it from a source won't work; it must be created where it will be used. Hospitals extract the 99Tc daughter product from the decay of the molybdenum isotope 99Mo. The 99Mo source has a half-life of 2.7 days, so it must be replaced weekly. A hospital receives a 20 GBq 99Mo source.

What is its activity one week later?

Express your answer using two significant figures.

Answer 1

Answer:

Explanation:

Initial radioactivity =  20 GBq

half life of source Mo = 2.7 days

dN / dt = N₀ λ where dN / dt is initial activity , N₀ is initial number of atoms and λ is disintegration constant .

λ = .693 / half life

= .693 / 2.7

= .257

dN / dt = N₀ λ

20k = N₀ x .257

N₀ = 20 k /.257

$N = N_0e^{-\lambda t }$

= 20 k /.257  x $e^{-.257\times 7 }$

= 20k x .64383

dN / dt = N λ

dN / dt = 20k x .64383  x .257

= 3.3 GBq.