Question

If $20$gm of radioactive substance due to radioactive decy reduces to $10$gm in $4$ minutes then in what time $80$gm of the same substance will reduce to $10$gm?

• A. $7$min
• B. $12$min
• C. $16$min
• D. $20$min

Answer 1

The correct option is A $7$min

Mass of the radioactive sustance $=20gm$

Radio active deacay reduces to $10gm$

Time $=4minute=4\times 60=240s$

According to law, we can say that

$N+N_0{e}^{-\lambda t}\frac{N}{N_0}=e^{-\lambda t}\frac{10}{20}=e^{-\lambda \times 240}ln{2}^{-1}=-\lambda \times 240\lambda =-\frac{ln{2}^{-1}}{240}=2.88\times {10}^{-3}/s$

Now then again write the mass action law of radio active decay

$\frac{N}{N_0}=e^{-\lambda t}\frac{70}{80}=e^{-2.88\times {10}^{-3}\times t}ln\frac{7}{8}=-2.88\times {10}^{-3}tt=46sec=\frac{46sec}{60}=7min$