Carbon (Z = 6) with mass number 11 decays to boron (Z = 5). (a) Is it is 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?

Question

Philoid · Accepted Answer

Given, ⁶C decays to ⁵B.

(a) ¹¹₆C → ¹¹₅B + β⁺

So, it is β⁺ decay.

(b) t_1/2 = 20.3 min.

λ = min^-1

C_i = 0.9C˳, C_f = 0.1C˳

So,

⇒

Taking log_e both sides, we get

⇒

∴

So,