Concepts Of Physics MCQ Edition [Volume 2]PhysicsThe Nucleus

During a single average-life,

Options

Amore than half of the active nuclei decay
Bhalf of the active nuclei decay
Call of the nuclei decay
Dfewer than half of the active nuclei decay

Correct answer

A. more than half of the active nuclei decay

Step-by-step solution

The number of active nuclei remaining after time t is given by the radioactive decay law: N = N₀ e^ - t The average life (or mean life) of a radioactive substance is = 1 . Substituting t = = 1 in the decay equation: N = N₀ e^ - ( 1 ) = N₀ e⁻¹ = N₀ e Since e 2.718 , the number of remaining active nuclei is: N = N₀ 2.718 0.368 N₀ The number of nuclei that have decayed during this time is: N_ decayed = N₀ - N = N₀ - 0.368 N₀ = 0.632 N₀ This means approximately 63.2 % of the initial active nuclei decay during one avera

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