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

(a) The reaction is given by

`C_6 → B_5 + β^+ + "v"`

It is a β+ decay since atomic number is reduced by 1.

(b) Half-life of the decay scheme , `T_(1"/"2) = 20.3` minutes

Disintegration constant, `lambda = 0.693/T_(1/2) = 0.693/20.3  "min"^(-1)`

If t is the time taken by the mixture in converting, let the total no. of atoms be 100N_0.

	Carbon	Boron
Initial	90 N0	10 N0
Final	10 N0	90 N0

  N = N₀e^−λt
Here, N₀ = Initial number of atoms
N = Number of atoms left undecayed

`10N_0 = 90N_0e^(-lambdat)` (For carbon)

⇒ `1/9 = e^(-0.693/20.3 xx t)`

⇒ `"In" 1/9 = (-0.693)/20.3 t`

⇒ t = 64.36 = 64 min