Introduction

In nuclear chemistry and radioactivity, exam questions often test how alpha and beta emissions change mass number and atomic number, and whether the product is an isotope, isobar, isotone, or isomer. Understanding isobar formation by beta emission is crucial for CSIR NET, NEET, JEE, and other competitive exams that include nuclear chemistry.

Basic Concepts: Isobars, Alpha and Beta

Isobars are nuclides with the same mass number A but different atomic numbers Z.

Alpha emission (α): loss of a helium nucleus ²₄He; this decreases atomic number by 2 and mass number by 4.

Beta emission (β⁻): a neutron converts into a proton with emission of an electron and antineutrino; Z increases by 1, A remains constant.

Because beta decay changes Z but keeps A constant, parent and daughter nuclei in beta decay are always isobars.

Option-by-Option Analysis

Let the parent nucleus be ^Z_AX.

Option (a): 1 α emission

Alpha emission: ^Z_AX → ^Z-2_A-4Y + ²₄α

Change in mass number: A → A-4 (decreases by 4).

Change in atomic number: Z → Z-2.

Since both A and Z change and A is not conserved, the daughter is not an isobar of the parent. So, option (a) is incorrect.

Option (b): 2 β emissions (correct)

Each β⁻ emission: ^Z_AX → ^Z+1_AY + β⁻ + ν̅

After one β⁻: ^Z_AX → ^Z+1_AY

After two β⁻: ^Z_AX → ^Z+2_AY′

In both steps, mass number A stays the same, while Z increases by 2 overall. Thus the final product ^Z+2_AY′ has the same mass number but different atomic number, so it is an isobar of the parent. Therefore, option (b) 2 β emissions is correct.

Option (c): 1 α and 1 β emission

Apply the changes stepwise:

Alpha emission: ^Z_AX → ^Z-2_A-4X₁

Beta emission (β⁻) from the product: ^Z-2_A-4X₁ → ^Z-1_A-4Y

Net effect: Mass number: A → A-4. Atomic number: Z → Z-1. The final product has mass number A-4, not A, so it cannot be an isobar of the original nucleus. Hence, option (c) is incorrect.

Option (d): 2 α and 1 β emission

Apply each emission sequentially:

First α: ^Z_AX → ^Z-2_A-4X₁

Second α: ^Z-2_A-4X₁ → ^Z-4_A-8X₂

One β⁻: ^Z-4_A-8X₂ → ^Z-3_A-8Y

Net effect: Mass number: A → A-8. Atomic number: Z → Z-3. Mass number changes from A to A-8, so the daughter is not an isobar of the parent. Thus, option (d) is incorrect.

Why Only Beta Emission Gives Isobars

In beta decay, nucleon count (total protons + neutrons) remains the same, so the mass number does not change.

This change only redistributes neutrons and protons, making the daughter nuclide another element with the same A, fitting the definition of isobars.

In contrast, alpha decay removes two protons and two neutrons, directly lowering the mass number and preventing isobar formation with the parent.

This is why nuclear chemistry MCQs commonly state that “in β decay, mother and daughter nuclei are isobars,” and that alpha decay is the type of decay that does not produce an isobaric daughter.