Question

Find the missing value for the radioactive isotope. (Round your answer to two decimal places.)

Answer 1

Answer:

1.1289 grams ( approx )

Step-by-step explanation:

Since, the final quantity of an element which has half life of n periods,

$A=P(\frac{1}{2})^{\frac{t}{n}}$

Where,

P = initial quantity,

t = total number of periods,

Here, A = 1 gram, t = 1000 years, n = 5715 years,

By substituting the values,

$1 = P(\frac{1}{2})^\frac{1000}{5715}$

$\implies P = 2^\frac{1000}{5715}\approx 1.1289$ ( using calculator )

Hence, the initial quantity would be 1.1289 grams ( approx )