no 41 Q41 Fe + ions are accelerated through a potential difference of 500 V and are injected - English - Adjectives

Question

no 41

Q41 Fe + ions are accelerated through a potential
difference of 500 V and are injected normally into a homogeneous
magnetic field B of strength 20-0 mT Find the radius of
the circular paths followed by the isotopes with mass number 57 and
58 Take the mass of an ion = A(1 6 ×
10–27) kg where A is the mass number

Sandeep K. Gupta · Accepted Answer

Dear Student,

Given- Charge on Fe+= +e   , V=500 V , M1=57 ×1
6×10-27 kg     and M2=58 ×1
6×10-27 kg and  B=20
0×10-3 TBecause accelerating potential is same hence both the isotopes will have same kinetic energyK=qV  -----(1)Radius of circular orbit in terms of KE is given byr=mvqB=2mKqB=2m(qV)qB=1B2mVq   -----(2)For  M1=57 ×1
6×10-27 kg r1=1B2×57 ×1
6×10-27 kg ×Vq=120
0×10-32×57×1 6×10-27×5001
6×10-19=1 193×10-2m=1
193 cmFor  M2=M2=58 ×1
6×10-27 kg r2=1B2×58 ×1
6×10-27 kg ×Vq=120
0×10-32×58×1 6×10-27×5001
6×10-19=1 204×10-2m=1 204 cm

Regards