Question

Yttrium-90, Y90 , is a radioactive isotope used in the treatment of liver cancer. The half‑life of Y90 is 2.67 days. If a dose with an activity of 192 μCi is given to a patient, how many days will it take for the activity of Y90 in the patient to reach 3.00 μCi?

Answer 1

It takes 16.02 days for the activity of Y90

Further explanation

The atomic nucleus can experience decay into 2 particles or more due to the instability of its atomic nucleus.  

Usually radioactive elements have an unstable atomic nucleus.  

The main particles are emitted by radioactive elements so that they generally decay are alpha (α), beta (β) and gamma (γ) particles  

General formulas used in decay:  

$\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{T/t\frac{1}{2} }}}$

T = duration of decay  

t 1/2 = half-life  

N₀ = the number of initial radioactive atoms  

Nt = the number of radioactive atoms left after decaying during T time  

No=192 μCi

Nt=3 μCi

t1/2=2.67 days

$\tt 3=192(\dfrac{1}{2})^{\dfrac{T}{2.67}}\\\\\dfrac{1}{64}=\dfrac{1}{2}^{\dfrac{T}{2.67}}\\\\\dfrac{1}{2}^6=\dfrac{1}{2}^{\dfrac{T}{2.67}}\\\\6=\dfrac{T}{2.67}\\\\T=16.02~days$