Question

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

hours?

Answer 1

5.5 grams

Step-by-step explanation:

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

`N(t) = N_0((1)/(2))^(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((1)/(2))^(t)/(h)` <----- Half-life equation

`N(30) = (22)((1)/(2))^(30)/(15)` <----- Insert values

`N(30) = (22)((1)/(2))^2` <----- Simplify exponent

`N(30) = (22)(0.25)` <----- Solve
`((1)/(2) )^2`

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