A uniform magnetic field with a slit system as shown in Fig. is to be used as a momentum filter for highenergy charged particles. With a field B tesla, it is found than the filter transmits `alpha` each of energy 5.3MeV. The magnetic field is increased to 2.3 tesla and deuterons are passed into the filter. The energy of each deutrons are passed into the filter. The energy of each deutrons transmitted by the filter is ........... MeV.

Answer

14.0185

Explanation

Radius of circular path is given by
`R=(mv)/(Bq)=p/(Bq)=(sqrt(2Km))/(Bq)`
Radius in both the cases are equal. Therefore `sqrt((2K_(alpha)m_(alpha))/(Bq_(alpha))=(sqrt(2K_(d)m_(d)))/(2.3Bq_(d))`
`(q_(d))/(q_(alpha))=e/(2e)=1/2` and `(m_(alpha))/(m_(d))=4/2=2:.K_(d)((2.3q_(d))/(q_(alpha)))^(2)((m_(alpha))/(m_(d))).K_(alpha)`
`K_(d)=(2.3xx1/2)^(2)(2)(5.3)MeV, K_(d)=14.0185MeV`