What series of decays would allow you to turn Lead, Pb-207 into Gold, Au-199?

Two alpha particle decays and one beta particle decay.

Explanation:

If Lead Pb-207 is to turn into Gold, Au-199, there needs to be a drop in mass number from 207 to 199. That drop is 207 - 199 = 8.

Since the mass number of an alpha particle(⁴₂He) is 4, to lose 8 nuclear particles(neutron + proton), we need 8 particles/nucleus ÷ 4 particles per alpha particle nucleus = 2 alpha particles.

The nuclear equation is given below

²⁰⁷₈₂Pb → ¹⁹⁹₇₉Au + ⁴₂He + ⁴₂He

Note that the charge is not balance

82 ≠ 79 + 2 + 2 = 83

For this to be balanced, we need to lose a beta particle, ⁰₋₁e. So, our equation becomes

²⁰⁷₈₂Pb → ¹⁹⁹₇₉Au + ⁴₂He + ⁴₂He + ⁰₋₁e

So, series of decays would allow you to turn Lead, Pb-207 into Gold, Au-199 are two alpha particle decays and one beta particle decay.

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