   Question Answers

# A cyclotron's oscillation frequency is 10 MHz and the operating magnetic field is 0.66 T. If the radius of its dee is 60 cm, then the kinetic energy of the proton beam produced by the accelerator is ….A. 9 MeVB. 10 MeVC. 7 MeVD. 11 MeV  Hint: We will find out the mass of the proton from the given frequency and magnetic field. Then we will find an expression for the kinetic energy of particles coming out of the oscillator. Finally converting the energy into eV, we can have our answer.

Formula used:
$f=\dfrac{qB}{2\pi m}$
$E_k=\dfrac{q^2B^2R^2}{2m}$

Complete step by step solution:
The frequency of oscillation in a cyclotron is given by,
$f=\dfrac{qB}{2\pi m}$
Now, we know the frequency and the magnetic field B. From question, $B=0.66 T$ and $f=10 MHz$. Again, charge of a proton is equal and opposite to the charge of an electron and is given as $q=1.6 \times 10^{-19} C$ .
So, after putting all this values in the above formula, we obtain the mass of the proton as,
$m=\dfrac{qB}{2\pi f}=1.68\times 10^{-27}kg$
Now, the condition for uninterrupted oscillation in the cyclotron is that the magnetic force on the proton has to be equal to the centrifugal force of its rotation. So,
$qvB=\dfrac{mv^2}{r}$
Here, v is the velocity of the proton and r is the radius of its orbit. After a little modification the formula becomes, $mv=qBr$. It gives the momentum of the proton.
Now, when the proton is about to leave the dee, $r=R$. Here R is the radius of the dee and it’s about 60 cm or 0.6 m here. So, the final kinetic energy is given by,
$E_k=\dfrac{(mv)^2}{2m}=\dfrac{q^2B^2R^2}{2m}=1.19\times 10^{-12}J=7.47 MeV$
Hence, among the given options, option C is the closest to the actual value. Hence, option C is the correct answer.

We cannot accelerate electrons in the normal cyclotron. An electron in high velocity changes its mass and this destroys the equilibrium condition. So, a fixed frequency cyclotron cannot accelerate electrons.

Note: Remember few things,
1. Make sure you convert energy from Joule to electron volt by dividing it by electronic charge.
2. In a formula, keep all the quantities in the same unit system.
3. If you remember the mass of the proton, you don’t need to calculate it again.
View Notes
Forced Oscillation and Resonance  Oscillation  CBSE Class 11 Physics Kinetic Theory Formulas  The Difference Between an Animal that is A Regulator and One that is A Conformer  CBSE Class 11 Physics Work, Energy and Power Formulas  Relation Between the Length of a Given Wire and Tension for Constant Frequency Using Sonometer  Where There is a Will There is a Way Essay  CBSE Class 11 Physics Law of Motion Formulas  CBSE Class 11 Physics Systems of Particles and Rotational Motion Formulas  Work and Energy  Important Questions for CBSE Class 11 Physics Chapter 6 - Work, Energy and Power  Important Questions for CBSE Class 11 Physics Chapter 4 - Motion in a Plane  Important Questions for CBSE Class 11 Physics Chapter 13 - Kinetic Theory  Important Questions for CBSE Class 11 Physics Chapter 3 - Motion in a Straight Line  Important Questions for CBSE Class 11 Physics  Important Questions for CBSE Class 11 Physics Chapter 10 - Mechanical Properties of Fluids  Important Questions for CBSE Class 11 Physics Chapter 11 - Thermal Properties of Matter  Important Questions for CBSE Class 11 Physics Chapter 2 - Units and Measurement  Important Questions for CBSE Class 11 Physics Chapter 7 - Systems of Particles and Rotational Motion  Important Questions for CBSE Class 12 Physics Chapter 11 - Dual Nature of Radiation and Matter  CBSE Class 10 Hindi A Question Paper 2020  Hindi A Class 10 CBSE Question Paper 2009  Hindi A Class 10 CBSE Question Paper 2015  Hindi A Class 10 CBSE Question Paper 2016  Hindi A Class 10 CBSE Question Paper 2012  Hindi A Class 10 CBSE Question Paper 2010  Hindi A Class 10 CBSE Question Paper 2007  Hindi A Class 10 CBSE Question Paper 2013  Hindi A Class 10 CBSE Question Paper 2008  Hindi A Class 10 CBSE Question Paper 2014  RS Aggarwal Class 10 Solutions - Mean, Median, Mode of Grouped Data, Cumulative Frequency Graph and Ogive  NCERT Solutions for Class 11 Physics Chapter 6  NCERT Solutions for Class 11 Physics Chapter 13  NCERT Solutions for Class 11 Physics Chapter 4 – Motion In a Plane  NCERT Exemplar for Class 11 Physics Chapter 6 - Work, Energy and Power (Book Solutions)  NCERT Solutions for Class 11 Physics Chapter 6 Work, Energy and Power in Hindi  NCERT Solutions for Class 11 Physics Chapter 10  HC Verma Class 11 Physics Part-1 Solutions for Chapter 15 - Wave Motion and Waves on a String  NCERT Solutions for Class 11 Physics Chapter 4 Motion in a Plane In Hindi  Class 11 Physics NCERT solutions  