The proton of energy 1 MeV describes a circular path in plane at right angles to a uniform magnetic field of 6.28 × 10-4 T. The mass of the proton is 1.7 × 10-27 kg. The cyclotron frequency of the proton is very nearly equal to :

Question

The proton of energy 1 MeV describes a circular path in plane at right angles to a uniform magnetic field of 6.28 × 10-4 T. The mass of the proton is 1.7 × 10-27 kg. The cyclotron frequency of the proton is very nearly equal to : (A) 107 Hz (B) 105 Hz (C) 106 Hz (D) 104 Hz

Tardigrade Admin · Accepted Answer

Cyclotron frequency is given by v=(q B/2 π m) ∴ v =(1.6 × 10-19 × 6.28 × 10-4/2 × 3.14 × 1.7 × 10-27) = 0.94 × 104 ≈ 104 Hz

Q. The proton of energy $1 M e V$ describes a circular path in plane at right angles to a uniform magnetic field of $6.28 \times 1 0^{- 4} T$ . The mass of the proton is $1.7 \times 1 0^{- 27} k g$ . The cyclotron frequency of the proton is very nearly equal to :

10 $^{7}$ Hz

10 $^{5}$ Hz

10 $^{6}$ Hz

10 $^{4}$ Hz

Cyclotron frequency is given by
$v = \frac{qB}{2 πm}$
$∴ v = \frac{1.6 \times 1 0 ^{- 19} \times 6.28 \times 1 0 ^{- 4}}{2 \times 3.14 \times 1.7 \times 1 0 ^{- 27}}$
$= 0.94 \times 1 0^{4}$
$\approx 1 0^{4} Hz$

Q. The proton of energy 1MeV describes a circular path in plane at right angles to a uniform magnetic field of 6.28×10−4T. The mass of the proton is 1.7×10−27kg. The cyclotron frequency of the proton is very nearly equal to :

107 Hz

105 Hz

106 Hz

104 Hz