Question

Write symbolically the nuclear β⁺ decay process of `""_6^11C` Is the decayed product X an isotope or isobar of (`""_6^11C`)? Given the mass values m (`""_6^11C`) = 11.011434 u and m (X) = 11.009305 u. Estimate the Q-value in this process.

Answer 1

In β⁺ decay, the atomic number Z of the nucleus goes up by 1.

The nuclear β⁺ decay process of `""_6^11C` is `""_6^11C->""_5^11B+e^++v`

Given :

`(""_6^11C)`= 11.011434 u

m (X) =`(""_5^11B)`= 11.009305 u

Mass of an electron or positron = 0.000548 u

c = speed of light

The Q value of the nuclear masses of the `""_6^11C` is given as:

`Q=[m(""_6^11C)+m(m(X))+m_e]C^2`

If atomic masses are used instead of nuclear masses, then we have to add 6m_e in the case of ¹¹C and 5m_e in the case of ¹¹B

Hence, eq.(1) reduces to

`Q=[m(""_6^11C)-m(""_5^11B)-2m_e]C^2`

Q= [11.011434-11.009305-2x 0.000548]C²

Q = 0.001033 C² u

1 u = 931.5 Mev/C²

Q = 0.001033 x 931.5 = 0.962 Mev