9. How long will it take 120 grams of Strontium-90 to decay to 7.5 grams?
with steps pls

116 years

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

58750.08068 is the answer i think