How long will it take for a 750 mg sample of radium with a half life of 15 days to decay to exactly 68mg?

-48

-50

-52

-54

52 da

Step-by-step explanation:

Whenever a question asks you, "How long to reach a certain concentration?" or something similar, you must use the appropriate integrated rate law expression.

The integrated rate law for a first-order reaction is

ln ([A₀]/[A]) = kt

dа ta:

[A]₀ = 750 mg

[A] = 68 mg

t_ ½ = 15 da

Step 1. Calculate the value of the rate constant.

t_½ = ln2/k Multiply each side by k

kt_½ = ln2 Divide each side by t_½

k = ln2/t_½

= ln2/15

= 0.0462 da⁻¹

Step 2. Calculate the time

ln (750/68) = 0.0462t

ln11.0 = 0.0462t

2.40 = 0.0462t Divide each side by 0.0462

t = 52 da