Suppose a $$88226$$ Ra nucleus at rest and in ground state undergoes α$$-decay$$ to a $$86222$$ Rn nucleus in its excited state. The kinetic energy of the emitted α particle is found to be $$4.44$$ MeV. $$86222$$ Rn nucleus then goes to its ground state by γ$$-decay$$. The energy of the emitted γ photon is $$____$$ keV.[Given : atomic mass of $$88226$$ Ra $$=$$ $$226.005$$ u, atomic mass of $$86222$$ Rn $$=$$ $$222.000$$ u, atomic mass of α particle $$=$$ $$4.000$$ u, $$1$$ u $$=$$ $$931$$ $$MeV/c2$$, c is speed of the light]

Question

Suppose a   $$88226$$ Ra nucleus at rest and in ground state undergoes  α$$-decay$$ to a   $$86222$$ Rn nucleus in its excited state. The kinetic energy of the emitted  α particle is found to be $$4.44$$ MeV.   $$86222$$ Rn nucleus then goes to its ground state by  γ$$-decay$$. The energy of the emitted  γ photon is $$____$$ keV.[Given : atomic mass of   $$88226$$ Ra $$=$$ $$226.005$$ u, atomic mass of   $$86222$$ Rn $$=$$ $$222.000$$ u, atomic mass of  α particle $$=$$ $$4.000$$ u, $$1$$ u $$=$$ $$931$$ $$MeV/c2$$, c is speed of the light]

Infinity Learn · Accepted Answer

$$88226Ra$$⇒$$86222Rn+24He$$Δ$$m=mRa$$−$$mRn+ma=226.005$$−$$(222+4)=0.005uQ$$ $$-$$ Value $$=5$$×$$10$$−$$3$$×$$931MeV=4.655MeV$$, Since, $$KE$$∝$$1m$$⇒ K.E. of $$86222Rn=4.44$$×$$4222=0.08MeV$$ Energy of γ$$=(4.655$$−$$4.44$$−$$0.08)MeV=135keV$$

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