Question

If T is the half-life of radioactive material, then the fraction that would remain after a time `"T"/2` is:

Options

• `1/2`

• `3/4`

• `1/sqrt2`

• `(sqrt2 - 1)/sqrt2`

Answer 1

`1/sqrt2`

Explanation:

Fraction remains after n half lives

`"N"/"N"_0 = (1/2)^"n" = (1/2)^("t"//"T")`

∴ `"N"/"N"_0 = (1/2)^((T//2)/"T")`

= `(1/2)^(1//2)`

= `1/sqrt2`