Respuesta :
The time taken for the substance to reach 12g is 7.8 days
The half-life of a substance is the time taken for it to reach half it's initial value.
I will list some formula and concepts which are of importance to this topic but not necessarily this question.
In solving this problem, we may need the formula to calculate half life of a substance which is given as.
[tex]T_\frac{1}{2}= In2/[/tex]λ
where λ = Disintegration constant.
Disintegration Constant
But to find this constant, we need to use another formula
[tex]N=N_oe^-yt\\\frac{N}{N_o}= e^-yt\\[/tex]
where the values are
- N = Mass of sample at time (t)
- No = Initial mass of sample
- λ = Disintegration constant
- t = time
Time Taken
However,
[tex]n=\frac{Log_e\frac{No}{N} }{Log_e2}[/tex]
Everything remains the same as above but only a slight change now
- n = number of half lives
Substituting the values,
[tex]n = \frac{Log_e(\frac{30}{12}) }{log_e2}\\n = 1.32[/tex]
Since n stands for the half life passed within time (t)
The time taken would be
[tex]t = 1.32 * 5.9\\t =7.8[/tex]
The time taken for the substance to reach 12g is 7.8 days.
Learn more about half-life here;
https://brainly.com/question/2320811
