Answer:
116 years
Step-by-step explanation:
To solve this, we will use the half life equation;
A(t) = A_o(½)^(t/t_½)
Where;
A(t) is the amount of strontium left after t years;
A_o is the initial quantity of strontium that will undergo decay;
t_½ is the half-life of strontium
t is the time it will take to decay
We are given;
A(t) = 7.5 g
A_o = 120 g
From online values, half life of strontium-90 is 29 years. Thus, t_½ = 29
Thus;
7.5 = 120 × ½^(t/29)
Divide both sides by 120 to get;
7.5/120 = ½^(t/29)
0.0625 = ½^(t/29)
In 0.0625 = (t/29) In ½
-2.772589 = (t/29) × (-0.693147)
(t/29) = -2.772589/(-0.693147)
t/29 = 4
t = 29 × 4
t = 116 years