Two neutral particles are kept 1m apart. Suppose by some machenism some charge is transferred from one particle to the other and the electric potential energy lost is completely converted into a photon. Calculate the longest and the next smaller wavelength of the photon possible. `h=6.63xx10^(-34)Js`.

Explanation

When charge q is transfered from one neutral particle are `q_(1)=+q and q_(2)=-q`. According to question eelctroc potential energy of the system is equal to the energy of photon emitted, So, `U=1/(4pi in_(0)) (q_(1)q_(2))/r=(hc)/lambda or lambda=(hc)/(q_(1)q_(2))xx4pi in_(0)r`
Case (i) `lambda` is maximum when charge transfered is minimum
`q_(1)=e=1.6xx10^(-19)C and q_(2)=-e=1.6xx10^(-19)C`
`:. lambda=((6.63xx10^(-34))xx(3xx10^(8)))/((1.6xx10^(-19))xx(1.6xx10^(-19)))xx1/(9xx10^(9))xx1=860m`
Case (ii) `lambda` is next to maximum when `q_(1)=+2e and q_(2)=-2e :. lambda=(hc)/((2e)(2e))xx4pi in_(0)r=860/4=215m`