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NEET2001PhysicsNuclear PhysicsActual

A certain radioactive element has a half-life of 20 years. If we have a block with 10 ~g of the element in it, after how many years will there be just 2.5 ~g of the element in the block?

Options

  1. A80 years
  2. B40 years
  3. C100 years
  4. D60 years.

Correct answer

B. 40 years

Step-by-step solution

aligned & T_ 1 / 2 =20 years & N₀=10 ~g & N=2.5 ~g N= & N₀ e^ - t = 0.693 T_ 1 / 2 e^ - t = & ( N N₀ ) t= & 1 ( N₀ N )= T_ 1 / 2 0.693 ( N₀ N ) = & 20 0.693 ( 10 2.5 )=40 years aligned

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