Answer:
Time = 6 years
Explanation:
First, we will calculate the no. of half life periods required to reduce the mass of Protactinium to the given value:
[tex]m' = \frac{m}{2^{n} } \\\\2^n = \frac{m}{m'}[/tex]
where,
n = no. of half-life periods = ?
m = initial mass = 86.3 g
m' = remaining mass = 10.8 g
Therefore,
[tex]2^n = \frac{86.3\ g}{10.8\ g}\\\\2^n = 8\\2^n = 2^3[/tex]
Since the bases are the same. Therefore equating powers:
n = 3
Now we calculate the time:
[tex]Time = (n)(Half-Life)\\Time =(3)(2\ years)[/tex]
Time = 6 years
