the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to…
the half - life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. starting with 150 grams of a radioactive isotope, how much will be left after 5 half - lives? use the calculator provided and round your answer to the nearest gram.
Answer
Explanation:
Step1: Identificar la fórmula
La cantidad de isótopo después de $n$ vidas medias está dada por $A = A_0\times\left(\frac{1}{2}\right)^n$, donde $A_0$ es la cantidad inicial y $n$ es el número de vidas medias. Aquí, $A_0 = 150$ gramos y $n = 5$.
Step2: Sustituir valores
$A=150\times\left(\frac{1}{2}\right)^5$.
Step3: Calcular $\left(\frac{1}{2}\right)^5$
$\left(\frac{1}{2}\right)^5=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{32}$.
Step4: Multiplicar por la cantidad inicial
$A = 150\times\frac{1}{32}=\frac{150}{32}= 4.6875$ gramos.
Step5: Redondear
Redondeando a la unidad más cercana, $A\approx5$ gramos.
Answer:
5 gramos