Chapter 19: Problem 34

Determine the symbol \({ }_{Z}^{A} \mathrm{X}\) for the parent nucleus whose \(\alpha\) decay produces the same daughter as the \({ }_{-1}^{0} \beta\) decay of \({ }^{220} \mathrm{At} .\)

Short Answer

Expert verified

\({ }_{88}^{224} \mathrm{Rn}\) is the parent nucleus.

Step by step solution

Understand Alpha Decay

In alpha decay, the parent nucleus emits an alpha particle. An alpha particle can be represented as \({ }_{2}^{4} \mathrm{He}\). The atomic number decreases by 2 and the mass number decreases by 4.

Understand Beta Decay

In beta decay, a neutron in the parent nucleus changes into a proton and an electron (beta particle) is ejected. Therefore, the atomic number increases by 1, represented as \({ }_{-1}^{0} \beta\), while the mass number remains the same.

Establish Parent Nucleus from Beta Decay

The given equation is the beta decay of astatine-220. It can be written as \({ }_{85}^{220} \mathrm{At}\) -> \({ }_{Z}^{A} \mathrm{X}\) + \({ }_{-1}^{0} \beta\). By applying the conservation of atomic numbers and mass numbers, we find X could be polonium (Po) with A=220 and Z=86.

Determine Parent Nucleus from Alpha Decay

Now, we know the alpha decay of the parent nucleus gives \({ }_{86}^{220} \mathrm{Po}\). So the equation is \({ }_{Z}^{A} \mathrm{X}\) -> \({ }_{86}^{220} \mathrm{Po}\) + \({ }_{2}^{4} \mathrm{He}\). Applying conservation laws, we find the parent nucleus could be radon (Rn) symbolized as \({ }_{88}^{224} \mathrm{Rn}\). Thus, the parent nucleus has Z=88 and A=224.

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Determine the symbol \({ }_{Z}^{A} \mathrm{X}\) for the parent nucleus whose \(\alpha\) decay produces the same daughter as the \({ }_{-1}^{0} \beta\) decay of \({ }^{220} \mathrm{At} .\)

Short Answer

Step by step solution

Understand Alpha Decay

Understand Beta Decay

Establish Parent Nucleus from Beta Decay

Determine Parent Nucleus from Alpha Decay

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