214Bi83 --> 214Po84 + eBismuth-214 undergoes first-order radioactive decay to polonium-214 by the release of a beta particle, as represented by the nuclear equation above. Which of the following quantities plotted versus time will produce a straight line?(A) [Bi](B) [Po](C) ln[Bi](D) 1/[Bi]

Option C. ln[Bi]

Explanation:

The nuclear equation of first-order radioactive decay of Bi to Po is:

²¹⁴Bi₈₃  →  ²¹⁴Po₈₄ + e⁻

The radioactive decay is expressed by the following equation:

     (1)  

where Nt: is the number of particles at time t, No: is the initial number of particles, and λ: is the decay constant.                

To plot the variation of the quantities in function of time, we need to solve equation (1) for t:

     (2)

Firts, we need to convert the number of particles of Bi (N) to concentrations, as follows:

                           (3)  

              (4)  

where : si the Avogadro constant and V is the volume.

Now, introducing equations (3) and (4) into (2), we have:

     (5)

Finally, from equation (5) we can get a plot of Bi versus time in where the curve is a straight line:

Therefore, the correct answer is option C. ln[Bi].

I hope it helps you!