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# An imaginary radioactive element decays to form elements X1,X2,X3,X4,X5 and X6, by ejecting two β-particles, followed by an α-particle, and again two (β-particles followed by an α -particle. What are the mass number and the atomic number of X6?

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Solution

## The symbolic representation of the reaction is: 9292Xβ−particle−−−−−−→X1β−particle−−−−−−→X2α−particle−−−−−−→X3β−particle−−−−−−→X4β−particle−−−−−−→X5α−particle−−−−−−→X6 In complete reaction, the total number of emitted a-particles = 2. ∴ Loss of the total mass number due to two α-particles = 4 + 4 = 8 ∴ Loss of atomic number due to two α -particles = 2 + 2 = 4 In a complete reaction, the total number of emitted β - particles = 4. ∴ Loss of mass number due to four β -particles = 0 Gain of atomic number due to four β−particles=1×4=4 ∴ Total loss of mass number = 8 Total loss or gain of atomic number = 4 - 4 = 0 ∴ Mass number of X6=(235−8)=227 Atomic number of X6=(92−0)=92

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