Question: Q. 1. A radioactive nucleus ’ $A$ ’ undergoes a series of given below :
$$ A \xrightarrow{\alpha} A_{1} \xrightarrow{\beta} A_{2} \xrightarrow{\alpha} A_{3} \xrightarrow{\gamma} A_{4} $$
The mass number and atomic number of $A_{2}$ are 176 and 71 respectively. Determine the mass and atomic numbers of $A_{4}$ and $A$. (ii) Write the basic nuclear processes underlying $\beta^{+}$ and $\beta^{-}$decays.
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Solution:
Ans. (i) $A_{4}$ Mass Number : 172
$A$ : Mass Number : 180
Atomic Number : 72
[Alternatively : Give full credit if student considers $\beta^{+}$decay and find atomic and mass numbers accordingly.]
${ }{72}^{180} \mathrm{~A} \xrightarrow{\alpha}{ }{70}^{176} A_{1} \xrightarrow{\beta}{ }^{176} A_{2} \xrightarrow{\alpha}{ }{69}^{172} A{3} \xrightarrow{\gamma}{ }{69}^{172} A{4}$
Gives the values quoted above.
If the student takes $\beta^{+}$decay
$$ { }{72}^{180} \mathrm{~A} \xrightarrow{\alpha}{ }^{176} A{1} \xrightarrow{\beta^{+}}{ }^{176} A_{2} \xrightarrow{\alpha}{ }^{172} 69 A_{3} \xrightarrow{\gamma}{ }^{172} A_{4} $$
This would give the answers :
$\left.\left(A_{4}: 172,69\right) ;(A 180,74)\right]$
(ii) Basic nuclear process for $\beta^{+}$decay
$$ p \rightarrow n+{ }_{1}^{0} e+v $$
For $\beta^{-}$decay
$$ n \rightarrow p+{ }_{-1}^{0} e+\bar{v} $$
[Note : Give full credit of this part, if student writes the processes as conversion of proton into neutron for $\beta^{+}$decay and neutron into proton for $\beta^{-}$decay.]
[CBSE Marking Scheme2017]
