Chapter 24, Problem 24.126P

Interpretation Introduction

Interpretation:

Product for electron capture by Gadolinium-146 has to be identified. Also the modes of decay and the two intermediate nuclides in the given series have to be predicted.

Concept Introduction:

Nuclides that are unstable generally decay in a mode that changes its N/Z ratio to the band of stability.

• Nuclides having many neutrons (Neutron-rich nuclides) have a high N/Z ratio and lies above the band of stability. Therefore, to decrease N/Z ratio these nuclides undergo ${\beta }^{-}$ decay.
• Nuclides having many protons (Proton-rich nuclides) have a low N/Z ratio and lies below the band of stability. Therefore, to increase N/Z ratio these nuclides undergo $e^{-}$ capture and/or ${\beta }^{+}$ decay. Heavier elements mostly undergo $e^{-}$ capture whereas lighter elements undergo ${\beta }^{+}$ emission.
• Nuclides having $Z>83$ are considered as too heavy to be stable. To decrease the values of Z and N, it undergoes $\alpha$ decay. Also some of the rare earth elements like ${}^{114}Nd,{}^{ 146}Sm,\mathrm{...}{ }^{174}Hf$ and light elements like ${}^{8}Li,{ }^{{}^9}Li\mathrm{...}$ undergo $\alpha$ decay.

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.