Question

Let's take a hypothetical radioactive nuclide sample of ${}^{80}X$.
It weighs 80 gm. Find the number of active nuclei remaining after a time of 0.5 second. Given its decay constant is 2 $s^{-1}$

• A. $6.023\times {10}^{23}/e$
• B. $6.023\times {10}^{23}$ x e
• C. $6.023\times {10}^{23}$
• D. $Noneofthese$

Answer 1

The correct option is A $6.023\times {10}^{23}/e$

Let's see what all is given to us.
Nuclide sample of ${}^{80}X$ weighing 80 gm.
Time elapsed 0.5 sec
Decay constant $\lambda$ = 2$s^{-1}$
What is being asked is the number of active nuclei left after given time duration.
$N=N_0{e}^{-\lambda t}$
I dunno $N_0$ . Can I find $N_0$ from what is given.

Yes!!!
80 gm of ${}^{80}X$ nuclide
Means a mole of it.
Means the sample has $6.023\times {10}^{23}$ Nucleus to begin with.
Let's put things together.
$N=6.023\times {10}^{23}\times e^{-0.5\times 2}N=6.023\times {10}^{23}/e$