Question

PLE help ASAP!

Answer 1

Answer:

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

Step-by-step 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;

$y = a \cdot (0.5)^{\dfrac{t}{h} }$

Which is of the form;

$N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}$

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;

$28 = 390 \times(0.5)^{\dfrac{t}{6} }$

$(0.5)^{\dfrac{t}{6} } = \dfrac{28}{390}$

Therefore;

$\dfrac{t}{6} \times ln\left(0.5} \right) = ln \left(\dfrac{28}{390} \right)$

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.