Question 305: Atoms & Nuclei

Question

Half-lives of two radioactive elements $$A$$ and $$B$$ are $$20$$ minutes and $$40$$ minutes, respectively. Initially, the samples have equal number of nuclei. After $$80$$ minutes, the ratio of decayed number of $$A$$ and $$B$$ nuclei will be:

Accepted Answer

For $${A_{t{aise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}} = 20\,\,$$ min, $$t=80$$ min, number of half lifes $$n=4$$
$$	herefore$$ Nuclei remaining $$ = {{{N_0}} \over {{2^4}}}.$$ Therefore nuclei decayed
$$ = {N_0} - {{{N_0}} \over {{2^4}}}$$
For $${B_{t{aise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}} = 40\,\,$$ min, $$t=80$$ min, number of half lifes $$n=4$$
$$	herefore$$ Nuclei remaining $$ = {{{N_0}} \over {{2^2}}}.$$ Therefore nuclei decayed
$$ = {N_0} - {{{N_0}} \over {{2^2}}}$$
$$	herefore$$ Required ratio
$$ = {{{N_0} - {{{N_0}} \over {{2^4}}}} \over {{N_0} - {{{N_0}} \over {{2^2}}}}}$$
$$ = {{1 - {1 \over {16}}} \over {1 - {1 \over 4}}}$$
$$ = {{15} \over {16}} 	imes {4 \over 3} = {5 \over 4}$$

Answer

$$1:4$$

Answer

$$5:4$$

Answer

$$1:16$$

Answer

$$4:1$$

Atoms & Nuclei

Half-lives of two radioactive elements $A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed number of A and B$ nuclei will be:

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