Answer: The remaining sample of X is 6.9 grams.
Explanation:
All the radioactive reactions follow first order kinetics.
The equation used to calculate rate constant from given half life for first order kinetics:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
We are given:
[tex]t_{1/2}=4.7min[/tex]
Putting values in above equation, we get:
[tex]k=\frac{0.693}{4.7min}=0.147min^{-1}[/tex]
The equation used to calculate time period follows:
[tex]N=N_o\times e^{-k\times t}[/tex]
where,
[tex]N_o[/tex] = initial mass of sample X = 78 g
N = remaining mass of sample X = ? g
t = time = 16.5 min
k = rate constant = [tex]0.147min^{-1}[/tex]
Putting values in above equation, we get:
[tex]N=78\times e^{-(0.147min^{-1}\times 16.5min)}\\\\N=6.9g[/tex]
Hence, the remaining amount of sample X is 6.9 g
