GATE Exam > GATE Questions > The frequency of a cyclotron oscillator is 10...
Start Learning for Free
The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .
- a)1.2x10-12J
- b)2.4 x 10-12J
- c)3.6 x 10-12 J
- d)4.8 x 10-12 J
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is ac...
The frequency of cyclotron f 107 Hz
for cyclotron
mv = Bqr
frequency
kinetic energy
for cyclotron
mv = Bqr
frequency
kinetic energy
Most Upvoted Answer
The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is ac...
Given data:
- Frequency of cyclotron oscillator: 107 Hz
- Radius of the cyclotron: 0.6 m
Formula:
The kinetic energy of a proton in a cyclotron is given by:
\[ E_k = qV \]
Where:
- \( E_k \) = Kinetic energy of the proton
- q = Charge of the proton = 1.6 x 10^-19 C
- V = Voltage of the cyclotron = \( 2qV = mω^2r^2 \)
Calculations:
1. First, calculate the angular frequency \( ω \) using the formula:
\[ ω = 2πf \]
\[ ω = 2π x 107 \]
\[ ω ≈ 672.73 \, rad/s \]
2. Now, substitute the values of \( ω \) and r into the equation for voltage:
\[ 2qV = mω^2r^2 \]
\[ 2 x 1.6 x 10^-19 x V = (1.67 x 10^-27) x (672.73)^2 x (0.6)^2 \]
\[ V = \frac{(1.67 x 10^-27) x (672.73)^2 x (0.6)^2}{2 x 1.6 x 10^-19} \]
\[ V ≈ 1593.6 \, V \]
3. Finally, calculate the kinetic energy of the proton using the formula:
\[ E_k = qV \]
\[ E_k = 1.6 x 10^-19 x 1593.6 \]
\[ E_k ≈ 2.54816 x 10^-16 \, J \]
Therefore, the kinetic energy of the proton beam produced by the accelerator will be approximately 1.2 x 10^-12 J.
- Frequency of cyclotron oscillator: 107 Hz
- Radius of the cyclotron: 0.6 m
Formula:
The kinetic energy of a proton in a cyclotron is given by:
\[ E_k = qV \]
Where:
- \( E_k \) = Kinetic energy of the proton
- q = Charge of the proton = 1.6 x 10^-19 C
- V = Voltage of the cyclotron = \( 2qV = mω^2r^2 \)
Calculations:
1. First, calculate the angular frequency \( ω \) using the formula:
\[ ω = 2πf \]
\[ ω = 2π x 107 \]
\[ ω ≈ 672.73 \, rad/s \]
2. Now, substitute the values of \( ω \) and r into the equation for voltage:
\[ 2qV = mω^2r^2 \]
\[ 2 x 1.6 x 10^-19 x V = (1.67 x 10^-27) x (672.73)^2 x (0.6)^2 \]
\[ V = \frac{(1.67 x 10^-27) x (672.73)^2 x (0.6)^2}{2 x 1.6 x 10^-19} \]
\[ V ≈ 1593.6 \, V \]
3. Finally, calculate the kinetic energy of the proton using the formula:
\[ E_k = qV \]
\[ E_k = 1.6 x 10^-19 x 1593.6 \]
\[ E_k ≈ 2.54816 x 10^-16 \, J \]
Therefore, the kinetic energy of the proton beam produced by the accelerator will be approximately 1.2 x 10^-12 J.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer?
Question Description
The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer?.
The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The frequency of a cyclotron oscillator is 107 Hz. The cyclotron is accelerating protons. If the radius of the does of the cyclotron be 0.6 m, the kinetic energy of the proton beam produced by the accelerator will be nearly_______ .a)1.2x10-12Jb)2.4 x 10-12Jc)3.6 x 10-12 Jd)4.8 x 10-12 JCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup