Question

Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

• A. \( (M_x - M_z)<M_y \)
• B. \( (M_x - M_y)<M_z \)
• C. \( M_x>(M_y + M_z) \)
• D. \( M_x<(M_y + M_z) \)

Hint:

In nuclear reactions, mass is not conserved by itself but mass-energy is conserved. The mass of the products is always less than the mass of the reactants due to the release of binding energy.

Answer 1

The Correct Option is D

In a nuclear reaction, the mass of the system before the reaction must be greater than or equal to the mass of the system after the reaction (mass-energy conservation). The mass of the original nucleus \( X \) is always greater than the sum of the masses of the products \( Y \) and \( Z \). This is because some mass is converted to energy during the reaction, which is released as energy (binding energy of the products). Thus, the relation that holds true is: \[ M_x<(M_y + M_z) \] Final Answer: (D) \( M_x<(M_y + M_z) \)