A radioactive nucleus undergoes a series of decays according to the sequence {\X} \stackrel{\beta}{ ───▸} {\X}_1 { ───▸} ^{\alpha} {\X}_2 \stackrel{\alpha}{ ───▸} {\X}_3 \text{. } If the mass number and atomic number of X_3 are 172 and 69 respectively, what is the mass number and atomic number of X ?

ICSE Class 10 Physics 2013 Solved Paper - Question 31

Question : 31 of 70

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A radioactive nucleus undergoes a series of decays according to the sequence

{\X} \ { ───▸}↖{β} {\X}_1 \ { ───▸} ↖{α} {\X}_2 { ───▸}↖{α} {\X}_3 \;\text ". "\;

If the mass number and atomic number of

X_3

are 172 and 69 respectively, what is the mass number and atomic number of

X

Solution:

{ }_{ {\Z}}^{ {\A}} {\X} {{  ───▸}}↖{β}{ }_{ {\Z}+1}^{ {\A}} {\X}_1 {{  ───▸}}↖{α} ^{{ {\A}-4}}_{{ {\Z}+1-2}} {\X}_2

{{  ───▸}}↖{α} ^{{ {\A}-4-4}}_{{ {\Z}+1-2-2}} {\X}_3

Given : Atomic number of

{\X}_3=69

and mass number of

{\X}_3=172

i.e.

{ }_{69}^{172} {\X}_3

{ }_{72} {\X}^{180} {{  ───▸}}↖{β}{ }_{73} {\X}_1{ }^{180} {{  ───▸}}↖{α}{ }_{71} {\X}_2{ }^{176} {  ───▸}↖{α}{ }_{69} {\X}_3{ }^{172}

Mass number of

X=180

Atomic number of

X=72

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