Question

The isotope sodium-24 has a half-life of 15 hours. Starting with 22 grams, how much remains in 30

Answer 1

Answer:

5.5 grams

Explanation:

To find how much of the isotope remains, you need to use the half-life equation:

$N(t) = N_0(\frac{1}{2})^\frac{t}{h}$

In this equation,

-----> N(t) = remaining mass (g)

-----> N₀ = initial mass (g)

-----> t = time (hrs)

-----> h = half-life (hrs)

You can find the remaining mass by plugging the given values into the equation and solving.

N(t) = ? g                          t = 30 hrs

N₀ = 22 g                         h = 15 hrs

$N(t) = N_0(\frac{1}{2})^\frac{t}{h}$                                         <----- Half-life equation

$N(30) = (22)(\frac{1}{2})^\frac{30}{15}$                                    <----- Insert values

$N(30) = (22)(\frac{1}{2})^2$                                      <----- Simplify exponent

$N(30) = (22)(0.25)$                                   <----- Solve $(\frac{1}{2} )^2$

$N(30) = 5.5$                                              <----- Multiply 22 and 0.25