Question

if you have 10 grams of a substance that decays with a half life of 14 days then how much will you have after 70 days?

Answer 1

Answer: The amount of substance left will be 0.316 grams.

Explanation:

All the decay processes follow first order kinetics.

The equation used to calculate half life for first order kinetics:

$t_{1/2}=\frac{0.693}{k}$

where,

$t_{1/2}$ = half life of the reaction = 14 days

k = ?

Putting values in above equation, we get:

$k=\frac{0.693}{14days}=0.0495days^{-1}$

Rate law expression for first order kinetics is given by the equation:

$t=\frac{2.303}{k}\log\frac{a}{y}$

where,

k = rate constant  = $0.0495days^{-1}$

t = time taken for decay process = 70 days

a = initial amount of the reactant  = 10 grams

y = amount left after decay process  = ? grams

Putting values in above equation, we get:

$70days=\frac{2.303}{0.0495days^{-1}}\log\frac{10g}{y}\\\\y=0.316g$

Hence, the amount of substance left will be 0.316 grams.

Answer 2

Answer: If it has a 1/2 life of 14 days, after 14 days there will be half of it left correct?  

Explanation:So, how many half-lifes are in 42 days?  

42 / 14 = 3  

This means it will divide 3 times.  

1st half life period: 10 / 2 = 5g  

2nd period: 5 / 2 = 2.5g  

3rd period: 2.5 / 2 = 1.25g

10 g at start, 5 g at 14 days, 2.5 g at 28 days, 1.25 g at 42 days.