Question

Carbon (Z = 6) with mass number 11 decays to boron (Z = 5). (a) Is it a β+-decay or a β−decay? (b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11?

Answer 1

Explanation:

(a) The reaction is shown as C6 → B5 +v + β+  

It can be noted that there is a reduction of atomic number by 1, it is a β+ decay.

(b) Decay scheme’s half-life, T1/2 = 20.3 minutes

Constant of disintegration, λ = 0.693T12 = 0.69320.3 min-1

Let’s consider that t is the time taken for the conversion by the mixture, let 100N0 be the total no. of atoms.

Initially, there will be 90 N0 of carbon and 10 N0 of boron. Finally, there will be 10 N0 will be carbon and 10 N0 of boron.  

Then, the equation is N = N0e− λt.

Here, N0 = Number of atoms in the initial stage

N = Undecayed atoms left  

For carbon, 10N0 = 90N0e−λt  

$\Rightarrow 19=e-0.69320 .3 \times t$

⇒ t = 64.36 = 64 min