Question

Let N be the number of b particles emitted by 1 gram of Na radioactive nuclie (half life=15 hrs)in $7.5$ hours N is :

• A. $6.2x{10}^{21}$
• B. $7.5x{10}^{21}$
• C. $1.25x{10}^{22}$
• D. $1.75x{10}^{22}$

Answer 1

Answer: (B)

$7.5x{10}^{21}$

$\frac{dN}{dt}=kN$

$N=-kt$

$N=N_o{e}^{-kt}$

given $N=\frac{N}{2}$ when $t=t_{\frac{1}{2}}$

$k=\frac{ln2}{t_{\frac{1}{2}}}$

the remaining molecules left after $t=7\frac{1}{2}$

$N=N_o{e}^{-k7\frac{1}{2}}$

$N=\frac{N_o}{\sqrt{2}}$

$N_o-\frac{N_o}{\sqrt{2}}=\frac{\sqrt{2}-1}{\sqrt{2}}\frac{1}{24}\times 6.023\times {10}^{23}$

$7.34\times {10}^{21}$