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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