Question
Sulphur $$ = 35\left( {34.96903\,u} \right)$$ emits a $$\beta $$ - particle but no $$\gamma - ray.$$ The product is chlorine $$ = 35\,\left( {34.96885\,u} \right).$$ The maximum energy emitted by the $$\beta $$ - particle is
A.
16.758$$\,MeV$$
B.
1.6758$$\,MeV$$
C.
0.16758$$\,MeV$$
D.
0.016758$$\,MeV$$
Answer :
0.16758$$\,MeV$$
Solution :
\[\underset{\left( Mass=34.96903\,u \right)}{\mathop{_{16}{{S}^{35}}}}\,\,\xrightarrow{-\beta }\,\underset{\left( Mass=34.96885\,u \right)}{\mathop{_{17}C{{l}^{35}}}}\,\]
$$\eqalign{
& {\text{Mass defect}} = \left( {34.96903 - 34.96885} \right)\,u \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.00018\,u \cr
& {\text{Energy emitted}} = 0.00018 \times 931\,MeV \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.16758\,MeV \cr} $$