A uniform magnetic field with a slit system as shown in fig.is to be used as a momentum filter for high-energy charged particles' With a field Btesla' it is found that the filter transmits $α$ -particles each of energy 5 3 MeV. The magnetic field is increased to
2.3 B tesla and deuterons are passed into the filter' The energy of each deuteron transmitted by the filter is

Question

A uniform magnetic field with a slit system as shown in fig.is to be used as a momentum filter for high-energy charged particles' With a field Btesla' it is found that the filter transmits $α$ -particles each of energy 5 3 MeV. The magnetic field is increased to

2.3 B tesla and deuterons are passed into the filter' The energy of each deuteron transmitted by the filter is

Infinity Learn · Accepted Answer

$$Heremv2R=qvB$$  or  $$mv=p=qBRso$$, Energy $$E=p22m=q2B2R22mE$$α$$=4e2$$×$$B2$$×$$R22$$×$$4mp$$,$$mp=$$ massofproton $$Ed=e2$$×$$(2$$⋅$$3B)2$$×$$R22$$×$$2mp$$∴ EdEα$$=(2$$⋅$$3)22$$  or  $$Ed=(2$$⋅$$3)2$$×$$5$$⋅$$32$$ $$=14MeV$$

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