The half life of a stream of radioactive particles moving along a straight path with a constant kinetic energy of 4 eV is 1 minute. The percentage of particles which decay before travelling a distance of 3.6 ~km is (Mass of the radioactive particles =3.2 10⁻²¹ ~kg and charge of the electron =1.6 10⁻¹⁹ C ).

Step-by-step solution

aligned & As, K . E .= 1 2 m v^2 V = 2 K . E . m & V = 2 4 16 10⁻¹⁹ 32 10⁻²¹ = 2 4 2 10⁻² & V =20 ~m / s aligned Time to travel a distance of 3.6 ~km is aligned & t= D v = 3.6 1000 20 s= 3.6 1000 20 60 ~min & =3 ~min =3 half-time aligned In three half life times, the number of particles decayed aligned & = N ₀- N ₀ 2^3 = 7 8 ~N ₀ & % req. = 7 8 ~N ₀ ~N _ o 100=87.5 % aligned