Question

If 1.000 g of 226^88Ra produces 0.0001 mL of the gas 222^86Rn at STP in 24 hours, what is the half-life of 226Ra in years?

a) 1620 years
b) 1800 years
c) 2000 years
d) 2200 years

Answer 1

The half-life of 226Ra is 1600 years.

Step-by-step explanation:

To find the half-life of 226Ra, we can use the information given in Example 11.3.3 which states that the half-life of 226Ra is 1600 years.

We can use the formula for radioactive decay to calculate the time it will take for 1.000 g of 226Ra to decay to 0.100 g:

t = t1/2 x log(N0/N) where t is the time, t1/2 is the half-life, N0 is the initial amount, and N is the final amount. Substituting the values, we get:

t = 1600 years x log(1.000 g/0.100 g) = 1600 years x log(10) = 1600 years x 1 = 1600 years.

Therefore, the half-life of 226Ra is 1600 years, which corresponds to option a) in the choices given.