Q10 / 97 · NTA Abhyas (JEE Main) 2020 · Physics · Nuclear Physics

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.

  • Correct answer
    A
    3.96×10-6
     
  • B
    3.90×10-6
     
  • C
    3.85×10-6
     
  • D
    4.86×10-6
     

Solution

From the given kinetic energy of the neutrons we first calculate their velocity. Thus

         12mv2=0.0327×1.6×10-19

∴        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,

          Δt=102500=4×10-3 s⁡

The fraction of neutrons decayed in time Δt second is,

          ΔN⁡N⁡=λΔt

Also,    λ = 0 . 6 9 3 T⁡ 1 / 2

∴        Δ N⁡ N⁡ = 0 . 6 9 3 T⁡ 1 / 2 Δ t = 0 . 6 9 3 7 0 0 × 4 × 1 0 - 3 = 3 . 9 6 × 1 0 - 6

Hence, the correct answer is option: 'A'.

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