Question

Half life of a radioactive element is 160 days. After 800 days, 1 g of element will reduce to (Radioactive decay follow
first order kinetics)

Answer 1

Answer:

The concentration after 800 days is 0.0313 g

Given:

Half-life = 160 days

Amount of radioactive material = 1 g

Solution:

Let us assume concentration after 800 days be x

n = Half-life of the reactant

Half-life for the first order reaction is given as,  

$t_{\frac{1}{2}}=\frac{0.639}{k}$

$k=\frac{0.639}{160}$

$k=0.00433 \ d a y s^{-1}$

Where,

k = Radioactive constant  

Now equation for the first order reaction is given as,

t=\frac{2.303}{k} \log \left(\frac{A_{o}}{A}\right)

Where,

$A_o$ = Initial concentration of element

A = Concentration of element at time t

$800=\frac{2.303}{0.00433} \log \left(\frac{1}{x}\right)$

$1.50413=\log 1-\log (x)$

We know that, log (1) = 0

$1.50413 =0-log (x)$

$Antilog (-1.50413) = x$

$x =0.0313 \ g$