Question

Radium-226 has a half-life of 1,600

years. How many grams of an 88
gram sample of radium-226
would remain after 4,800 years?

Answer 1

11 grams

Step-by-step explanation:

To find the remaining mass of radium-226, you need to use the half-life formula:

`A = A_0 *((1)/(2))^{(t)/(h)`

In this formula,

-----> A = remaining mass (g)

-----> A₀ = initial mass (g)

-----> t = time passed (yrs)

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

You can plug the given values into the formula and solve to find the remaining mass (A).

A = ? g t = 4,800 yrs

A₀ = 88 g h = 1,600 yrs

`A = A_0 *((1)/(2))^{(t)/(h)` <----- Half-life formula

`A = (88)*((1)/(2))^(4,800)/(1,600)` <----- Insert values

`A = (88)*((1)/(2))^ 3` <----- Divide 1,600 from 4,800

`A = (88)*(0.125)` <----- Raise
`(1)/(2)` to the power of 3

`A = 11` <----- Multiply 88 and 0.125