Iodine-131 half life 8.040 how long will it take for a 40 gram sample of iodine-131 to decay to 0.75 grams

See explanation below

Explanation:

To get this, we need to apply the general expression for half life decay:

N = N₀e(-λt)    (1)

Where:

N and N₀ would be the final and innitial quantities, in this case, masses.

t: time required to decay

λ: factor related to half life

From the above expression we need λ and t. To get λ we use the following expression:

λ = t₁₂/ln2   (2)

And we have the value of half life, so, replacing we have:

λ = 8.04 / ln2 = 11.6

Now, we can replace in (1) and then, solve for t:

0.75 = 40 exp(-11.6t)

0.75 / 40 = exp(-11.6t)

ln(0.01875) = -11.6t

-3.9766 = -11.6t

t = -3.9766 / -11.6