Answer: The correct answer is Option 3.
Explanation:
All the radioisotope decay processes follow first order kinetics.
Rate law expression for first order kinetics is given by the equation:
[tex]k=\frac{2.303}{t}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = ?
t = time taken for decay process = 8.32 seconds
a = initial amount of the reactant = 80 mg
a - x = amount left after decay process = 20 mg
Putting values in above equation, we get:
[tex]k=\frac{2.303}{8.32sec}\log\frac{80g}{20}\\\\k=0.166sec^{-1}[/tex]
The equation used to calculate half life for first order kinetics:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
where,
[tex]t_{1/2}[/tex] = half life of the reaction = ?
k = [tex]0.166sec^{-1}[/tex]
Putting values in above equation, we get:
[tex]t_{1/2}=\frac{0.693}{0.166sec^{-1}}=4.16sec[/tex]
Hence, the correct answer is Option 3.
Answer:
4.16s
Explanation:
N = 20*10⁻³g
N₀ = 80*10⁻³g
t = 8.32
N = N₀e⁻λt
In(N/N₀) = -λt
-λ = 1/t * In(N/N₀)
-λ = 1 / 8.32 * In (20*10⁻³ / 80*10⁻³)
-λ = 0.12 * In(0.25)
-λ = -0.167
λ = 0.167
t½ = 0.693 / λ
t½ = 0.693 / 0.167
t½ = 4.16s
