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13.Nuclei
medium
Substance $A$ has atomic mass number $16$ and half life of $1$ day. Another substance $B$ has atomic mass number $32$ and half life of $\frac{1}{2}$ day. If both $A$ and $B$ simultaneously start undergo radio activity at the same time with initial mass $320\,g$ each, how many total atoms of $A$ and $B$ combined would be left after $2$ days $.........\times 10^{24}$
A
$3.38$
B
$6.76$
C
$67.6$
D
$1.69$
(JEE MAIN-2023)
Solution
$\left( N _0\right) A =\frac{320}{16}=20 \text { moles }$
$\left( N _0\right) B =\frac{320}{32}=10 \text { moles }$
$N _{ A }=\frac{\left( N _0\right)_{ A }}{(2)^{2 / 1}}=\frac{20}{4}=5$
$N _{ B }=\frac{\left( N _0\right)_{ B }}{(2)^{2 / 5}}=\frac{10}{2^4}=0.625$
Total $N =5.625$
No. of atoms $=5.625 \times 6.023 \times 10^{23}$
Standard 12
Physics
