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((1)/(2))^{t/t(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(1)/(2)^(T/t1/2)\\\\Nt=8.5(1)/(2)^(180/60)\\\\Nt=8.5((1)/(2))^3\\\\Nt=1.0625~mg`