Question: Q. 5. (i) Write the process of $\beta^{-}$-decay. How can radioactive nuclei emit $\beta^{-}$particles even though they do not contain them? Why do all electrons emitted during $\beta^{-}$decay not have the same energy?
(ii) A heavy nucleus splits into two lighter nuclei. Which one of the two - parent nuclei or the daughter nuclei has more binding energy per nucleon?
[Foreign II 2017]
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Solution:
Ans. (i) A nucleus, that spontaneously decays by emitting an electron, or a positron, is said to undergo $\beta$ decay
[Alternatively, ${ }{\mathrm{Z}}^{\mathrm{A}} X \rightarrow{ }{\mathrm{Z}+1}^{\mathrm{A}} Y+e^{-}+\overline{\mathrm{v}}$ (antineutrino)
${ }{\mathrm{Z}}^{\mathrm{A}} X \rightarrow{ }{\mathrm{Z}-1}^{\mathrm{A}} Y+e^{+}+\mathrm{v}$ (neutrino)
(Any one) 1
During $\beta$ decay, nucleons undergo a transformation.
$$ n \rightarrow p+e^{-}+\bar{v} $$
A neutron converts into a proton and an electron.
[Alternatively,
$$ \begin{equation*} p \rightarrow n+e^{+}+v \tag{1} \end{equation*} $$
A proton converts into a neutron and a positron] It is because the neutrinos, or antineutrino, carry off different amounts of energy.
(ii) The daughter nuclei have more binding energy per nucleon.
[CBSE Marking Scheme 2017]
Detailed Answer :
(i) Kindly refer ‘Revision Notes’ of this topic for description of $\beta$-decay.
Radioactive nuclei can emit $\beta$-particles i.e., electrons or positrons even though they do not contain them. The reason is that neutron or proton present in the nucleus get interconverted and emitting electron or positron.
Electrons or positrons are emitted in $\beta$-decay process along with neutrino or antineutrino. The energy of these emitted neutrino or antineutrino are different which effect the energy of electrons or positrons.
