Question

U-238 which has a long half-life is also find the ages of geological formations (rocks). Meanwhile I-131, which has much shorter half-life, is used for diagnosing thyroid disorders. What is the mass of an original 5.6 gram sample of I-131 that is still radioactive after 16.042 days?

Answer 1

The mass after 16.042 days : 1.4 g

Further explanation

Given

mass of 5.6 gram sample of I-131

time=16.042 days

Required

The mass of a sample

Solution

General formulas used in decay:  

$\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{t/t\frac{1}{2} }}}$

T = duration of decay  

t 1/2 = half-life  

N₀ = the number of initial radioactive atoms  

Nt = the number of radioactive atoms left after decaying during T time  

Half-life of I-131 = 8 days

Input the value :

$\tt Nt=5.6.\dfrac{1}{2}^{16.042/8}\\\\Nt=\boxed{\bold{1.4~g}}}$