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


Sagot :

Answer:

5.5 grams

Explanation:

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

[tex]N(t) = N_0(\frac{1}{2})^\frac{t}{h}[/tex]

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

[tex]N(t) = N_0(\frac{1}{2})^\frac{t}{h}[/tex]                                         <----- Half-life equation

[tex]N(30) = (22)(\frac{1}{2})^\frac{30}{15}[/tex]                                    <----- Insert values

[tex]N(30) = (22)(\frac{1}{2})^2[/tex]                                      <----- Simplify exponent

[tex]N(30) = (22)(0.25)[/tex]                                   <----- Solve [tex](\frac{1}{2} )^2[/tex]

[tex]N(30) = 5.5[/tex]                                              <----- Multiply 22 and 0.25