Question

Sodium-25 was to be used in an experiment, but it took 3.0 minutes to get the sodium from the reactor to the laboratory. If 8.0 mg of sodium-25 was removed from the reactor, how many mg of sodium-25 were placed in the reaction vessel 3.0 minutes later if the half life of sodium-25 is 60 seconds.

Answer 1

Sodium-25 after 3 minutes : 1.0625 mg

Further explanation

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=8 mg

t1/2=60 s

T=3 min=180 s

$\tt Nt=No\dfrac{1}{2}^{T/t1/2}\\\\Nt=8.5\dfrac{1}{2}^{180/60}\\\\Nt=8.5(\dfrac{1}{2})^3\\\\Nt=1.0625~mg$