Question

PLE help ASAP!

Element X decays radioactively with a half life of 6 minutes. If there are 390 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 28 grams?
y =
= a(.5)^ t/h

Answer 1

The time it would take the element to decay to 28 grams is approximately 22.5 minutes

Explanation:

The give half life of element X = 6 minutes

The given initial mass of the radioactive element X = 390 grams

The mass of the element X after decay = 28 grams

The function that represent the decay of element X is given as follows here;

`y = a \cdot (0.5)^{(t)/(h) }`

Which is of the form;

`N(t) = N_0 \left ((1)/(2) \right )^{(t)/(t_(1/2))`

Therefore;

h = 6 minutes = The time duration of the half life

a = N₀ = The initial mass = 390 g

N(t) = The final mass = 28 g

t = The time it takes the element to decay

Plugging in the values gives;

`28 = 390 *(0.5)^{(t)/(6) }`

`(0.5)^{(t)/(6) } = (28)/(390)`

Therefore;

`(t)/(6) * ln\left(0.5} \right) = ln \left((28)/(390) \right)`

t/6 = ln(29/390)/ln(0.5)

t = 6 × ln(29/390)/ln(0.5) ≈ 22.496

Given the answer to the nearest tenth of a minute, the time it would take the element to decay to 28 grams, t ≈ 22.5 minutes.