If the maximum value of accelerating potentia | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The kinetic energy gained by a proton after $n$ revolutions in a cyclotron is given by $K = n 	imes (2qV)$,where $V$ is the maximum accelerating

Vedclass · Accepted Answer

$543$

Vedclass · Answer

(C) The kinetic energy gained by a proton after $n$ revolutions in a cyclotron is given by $K = n 	imes (2qV)$,where $V$ is the maximum accelerating potential per gap and there are two gaps per revolution.Given:$V = 12 	imes 10^3 \, V$$q = 1.6 	imes 10^{-19} \, C$$m_p = 1.67 	imes 10^{-27} \, kg$$v = \frac{c}{6} = \frac{3 	imes 10^8}{6} = 0.5 	imes 10^8 \, m/s$Equating the kinetic energy to the work done:$n(2qV) = \frac{1}{2} m_p v^2$$n = \frac{m_p v^2}{4qV}$$n = \frac{1.67 	imes 10^{-27} 	imes (0.5 	imes 10^8)^2}{4 	imes 1.6 	imes 10^{-19} 	imes 12 	imes 10^3}$$n = \frac{1.67 	imes 10^{-27} 	imes 0.25 	imes 10^{16}}{76.8 	imes 10^{-16}}$$n = \frac{0.4175 	imes 10^{-11}}{76.8 	imes 10^{-16}} \approx 543.6$Rounding to the nearest integer,the number of revolutions is $543$.

Similar Questions

The oscillator frequency of a cyclotron is $10 \,MHz$. What should be the operating magnetic field for accelerating protons (in $,T$)? (Given: mass of proton $m = 1.67 \times 10^{-27} \,kg$,charge of proton $q = 1.6 \times 10^{-19} \,C$)

Discuss the motion of a charged particle in a uniform magnetic field with initial velocity perpendicular to the magnetic field. $OR$ Explain the principle of a cyclotron.

The maximum velocity to which a proton can be accelerated in a cyclotron of $10\, MHz$ frequency and radius $50\, cm$ is

The oscillating frequency of a cyclotron is $10 \, MHz$. If the radius of its dee is $0.5 \, m$,the kinetic energy of a proton,which is accelerated by the cyclotron,is ...... $MeV$.

Assertion : Cyclotron is a device which is used to accelerate the positive ion.
Reason : Cyclotron frequency depends upon the velocity.

Vedclass Test Series

Exam Paper Generator

Online Exam Module