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# 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 - Physics

ConceptMass-Energy Relation and Mass Defect

#### Question

Carbon (Z = 6) with mass number 11 decays to boron (Z = 5). (a) Is it a β+-decay or a βdecay? (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?

#### Solution

(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 100N0.

 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

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Solution 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 Concept: Mass-Energy Relation and Mass Defect.
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