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There is a stream of neutrons with a kinetic energy of 0 . 0327 eV . If the half-life of the neutron is 700 second, what fraction of neutrons will decay before they travel a distance of 10 m ? Given the mass of neutron = 1 . 675 × 10 - 27 kg .

Options

  1. A3 . 96 × 10 - 6
  2. B3 . 90 × 10 - 6
  3. C3 . 85 × 10 - 6
  4. D4 . 86 × 10 - 6

Correct answer

A. 3 . 96 × 10 - 6

Step-by-step solution

From the given kinetic energy of the neutrons we first calculate their velocity. Thus 1 2 mv 2 = 0 . 0 3 2 7 × 1 . 6 × 1 0 - 1 9 ∴ v ⁡ 2 = 2 × 0 . 0 3 2 7 × 1 . 6 × 1 0 - 1 9 1 . 6 7 5 × 1 0 - 2 7 = 6 2 5 × 1 0 4 or v   =   2500   m   s - 1 With this speed, the time taken by the neutrons to travel a distance of 10 m is, Δ t = 1 0 2 5 0 0 = 4 × 1 0 - 3   s ⁡ The fraction of neutrons decayed in time Δt second is, Δ N &

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