Physics - Modern Physics Question with Solution | TestHub

The masses of parent and daughter elements nuclide are${\mathrm{m}}_1\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }{\mathrm{m}}_2$respectively.

Mass of parent element =${\mathrm{m}}_1+\mathrm{ }\mathrm{Z}{\mathrm{m}}_{\mathrm{e}}$(where Z is atomic number of parent element)

Mass of daughter element -${\mathrm{m}}_2+\mathrm{ }\left(\mathrm{Z}+1\right){\mathrm{m}}_{\mathrm{e}}\mathrm{ }$(As atomic number of element increases by one due to$\mathrm{\beta }\mathrm{ }–$emission)

Mass decay = mass of parent atom - one$\mathrm{\beta }$loss - [mass of daughter atom along with one electron]

${=\mathrm{m}}_1+\mathrm{Z}{\mathrm{m}}_{\mathrm{e}}-{\mathrm{m}}_{\mathrm{e}}-[{\mathrm{m}}_2+\mathrm{ }\left(\mathrm{Z}+1\right){\mathrm{m}}_{\mathrm{e}}]$

$=[{\mathrm{m}}_1-{\mathrm{m}}_2-2{\mathrm{m}}_{\mathrm{e}}]$

Energy liberated$=\left[{\mathrm{m}}_1-{\mathrm{m}}_2-\mathrm{ }2{\mathrm{m}}_{\mathrm{e}}\right]{\mathrm{c}}^2$