Question

Question #188b6

Answer 1

`"23 g"`

Explanation:

All you have to do here is to use the following equation

`A_t = A_0 * (1/2)^color(red)(n)`

Here

• `A_t` is the mass of the substance that remains undecayed after a period of time `t`
• `A_0` is the initial mass of the substance
• `color(red)(n)` represents the number of half-lives that pass in a given time period `t`

In your case, you know that the initial mass of the substance is equal to `"35 g"`.

Now, the number of half-lives that pass in a given time period `t` can be calculated by dividing the period of time by the half-life of the substance, `t_"1/2"`.

`color(red)(n) = t/t_"1/2"`

In your case, the number of half-lives that pass in `2100` years is equal to

`color(red)(n) = (2100 color(red)(cancel(color(black)("years"))))/(3400color(red)(cancel(color(black)("years")))) = 0.617647`

Plug this into the aforementioned equation and solve for `A_"2100 years"`, the mass of the substance that remains undecayed after `2100` years

`A_ "2100 years" = "35 g" * (1/2)^0.617647 = color(darkgreen)(ul(color(black)("23 g")))`

The answer is rounded to two **[sig figs](