Strontium-90 ( ) undergoes a radioactive decay chain that eventually produces stable…

PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation

Problem

Strontium-90 (

{}^{90}_{38}\text{Sr}

) undergoes a radioactive decay chain that eventually produces stable zirconium-90 (

{}^{90}_{40}\text{Zr}

). The chain proceeds through two successive beta decays: 1.

{}^{90}_{38}\text{Sr}

decays to

{}^{90}_{39}\text{Y}

. 2.

{}^{90}_{39}\text{Y}

decays to

{}^{90}_{40}\text{Zr}

. Each step emits exactly one lepton, and no other particles besides the daughter nuclei are produced. Assume the atomic electron clouds do not participate. For calculations, you may use

N_A = 6.0\times10^{23}\,\text{mol}^{-1}

and an atomic mass of

90\,\text{g mol}^{-1}

for all three nuclides. (a) For each of the two beta decays, write a balanced nuclear equation that includes the emitted lepton. Clearly label the lepton in each equation. (b) If one atom of

{}^{90}_{38}\text{Sr}

completes the entire two-step decay chain, state the type and quantity of leptons produced in total. (c) A sealed source initially contains

1.0\,\mu\text{g}

of pure

{}^{90}_{38}\text{Sr}

. Assuming every nucleus undergoes the full two-step chain, calculate the total number of antineutrinos that will be emitted by the time all nuclei have reached

{}^{90}_{40}\text{Zr}

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