a few days ago i got this problem: THERE IS A STREAM OF NEUTRONS WITH A KINETIC ENERGY OF 0.0327eV. IF THE HALF LIFE OF THE NEUTRONS IS 700 SECONDS, WHAT FRACTION OF NEUTRONS WILL DECAY BEFORE THEY TRAVEL A DISTANCE OF 10 km. the soln. asks to divide the total dist. ie 10 km by the initial velocity and thus after finding time , obtain the final no. of neutrons using the radioactivity eqn.......... but i have a different point of view....................................... please have a look at my logic. here there is no specific equation of reaction is given due to which i assume that the total energy of the neutrons remains constant.=> 1/2 Mtv2=constant=.0327ev ( Mt=mass of neutrons at any instant of time) =>as the total mass of the system changes spontanously even the velocity of the neutrons will change in such a way as to keep the product of 1/2 Mtv2=.0327ev=k(say) where Mt is the mass of the sample at any time t.hence vt=2k/Mt and Mt=M0e^-Yt(Y=lambda) hence i feel,(M0= initial mass) ds/dt=2k/M0e^-Yt =>ds= (2k/M0 )* e^Yt/2 dt =>ds= (2k/M0 )* e^Yt/2 dt [0 ][ 10000]ds=integration(from0 to t) (2k/M0 )* e^Yt/2 dt thus from this t can be obtained when the system covers 10000m and this t can be substituted in the eqn. Mt=M0e^(-Yt) to obtain (1-e^(-Yt)) which is actually the fraction of the no of neutrons decayed . Please Please Please do tell whether my logic is right or wrong..................... a request by punterjack...............................................................................

 

a few days ago i got this problem:

THERE IS A STREAM OF NEUTRONS WITH A KINETIC ENERGY OF 0.0327eV. IF THE HALF LIFE OF THE NEUTRONS IS 700 SECONDS, WHAT FRACTION OF NEUTRONS WILL DECAY BEFORE THEY TRAVEL A DISTANCE OF        10 km.

the soln. asks to divide the total dist. ie 10 km by the initial velocity and thus after finding time , obtain the final no. of neutrons using the radioactivity eqn.......... but i have a different point of view....................................... 

please have a look at my logic. here there is no specific equation of reaction is given due to which i assume that the total energy of the neutrons remains constant.=> 1/2 Mtv2=constant=.0327ev ( Mt=mass of neutrons at any instant of time)
=>as the total mass of the system changes spontanously even the velocity of the neutrons will change in such a way as to keep the product of 1/2 Mtv2=.0327ev=k(say) where Mt is the mass of the sample at any time t.hence
vt=2k/Mt  and Mt=M0e^-Yt(Y=lambda) hence i feel,(M0= initial mass)
ds/dt=2k/M0e^-Yt
=>ds= (2k/M0 )* e^Yt/2 dt
=>ds= (2k/M0 )* e^Yt/2 dt
[0 ][ 10000]ds=integration(from0 to t) (2k/M0 )* e^Yt/2 dt
thus from this t can be obtained when the system covers 10000m and this t can be substituted in the eqn.
Mt=M0e^(-Yt)  to obtain (1-e^(-Yt)) which is actually the fraction of the no of neutrons decayed .

Please Please Please do tell whether my logic is right or wrong.....................

a request by punterjack...............................................................................