Question

78 grams of a radioactive nuclei X undergoes radioactive decay. The half-life of X is 4.7 minutes. After 16.5 minutes, the remaining sample of X is approximately: 12.8g ; 8.4g ; 6.9g ; 5.5g ;

Answer 1

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:

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

We are given:

$t_{1/2}=4.7min$

Putting values in above equation, we get:

$k=\frac{0.693}{4.7min}=0.147min^{-1}$

The equation used to calculate time period follows:

$N=N_o\times e^{-k\times t}$

where,

$N_o$ = initial mass of sample X = 78 g

N = remaining mass of sample X = ? g

t = time = 16.5 min

k = rate constant = $0.147min^{-1}$

Putting values in above equation, we get:

$N=78\times e^{-(0.147min^{-1}\times 16.5min)}\\\\N=6.9g$

Hence, the remaining amount of sample X is 6.9 g