AIIMS 2018 Physics Decay Constant and Activity MCQ Question
The luminous dials watches are usually made by mixing a zinc sulphide phosphor with an α particle emitter. The mass of radium (mass number 226, half-life 1620 years) that is needed to produce an average of 10 α-particles per second for this purpose is
2.77 mg
2.77 g
2.77×10⁻²³ g
2.77×10⁻¹³ kg
Correct Answer
Detailed Explanation
To produce an average of 10 α-particles per second from radium-226 (²²⁶Ra), we can use the radioactive decay formula, which relates the activity (A) to the number of atoms (N) and the decay constant (λ). The decay constant can be calculated using the half-life (t₁/₂) of radium, leading to λ = 0.693/t₁/₂. For 10 α-particles per second, we find that N must be approximately 2.77 × 10¹² atoms, which corresponds to a mass of about 2.77 × 10⁻¹³ kg of radium-226, making option D correct.
Options A and B are incorrect as they represent masses that are too large for the required activity, while option C is too small and does not account for the necessary number of atoms to achieve the specified α-particle emission rate.
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