Question

Wonder Woman’s Golden Lasso is wielded by Princess Diana of Themyscira. While useful as a weapon, it also compels anyone it captures to tell the truth. Once wrapped around a person, the lasso very accurately monitors breathing, heart rate, and blood pressure. It does this by using both visible and higher energy X-ray light, which can penetrate human skin and monitor the dilation of capillary blood vessels. The element responsible for the lasso’s radiation has a half-life of 1.15E5 years. The lasso was formed from Aphrodite’s girdle and contained 110 mols of radioactive atoms (6.62E25 atoms) when it was created. Currently, the lasso contains 5.74E25 radioactive atoms. How old is the lasso?

a) 1780 years

b) 2400 years

c) 23,660 years)

d) 3100 years

e) 2650 years

Answer 1

initial number of atoms, N₀ = 6.62 x 10²⁵

current number of atoms, N = 5.74 x 10²⁵

half-life, t_1/2 = 1.15 x 10⁵ years

decay constant, λ = 0.6 93/ t_1/2 = 0.693/1.15 x 10⁵ = 0.602 x 10^-5 year^-1

using radioactive decay law, N = N₀ e^-λt

5.74 x 10²⁵ = 6.62 x 10²⁵ e^-λt

e^λt = 1.153

λt = ln1.153 = 0.142

time t = 0.142/λ = 0.142 /0.602 x 10^-5 = 23660 years

c) 23666 years