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.

Step-by-step 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)=(0.693)/(k)`

We are given:

`t_(1/2)=4.7min`

Putting values in above equation, we get:

`k=(0.693)/(4.7min)=0.147min^(-1)`

The equation used to calculate time period follows:

`N=N_o* e^(-k* 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* e^{-(0.147min^(-1)* 16.5min)}\\\\N=6.9g`

Hence, the remaining amount of sample X is 6.9 g