By Sunil Bhardwaj

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It is observed that when the projectile is moving with the energy of 20MeV then the mass of moving projectile (m) and the mass in the rest $$({ m }_{ 0 })$$ are equal. $$\therefore m = { m }_{ 0 }\qquad \qquad \qquad ...(below 20 MeV)$$ But in 1946, Lorenz found that when the projectile is moving with energy more than 20MeV, in that case the mass of the projectile is given by, $$m = \frac { { m }_{ 0 } }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } } \qquad \qquad \qquad ...(1)$$ where v = Velocity of projectile and c = Velocity of light.
As v < c $$\therefore \frac { v }{ c } < 1$$ or $$\frac { { v }^{ 2 } }{ { c }^{ 2 } } < 1$$ $$\therefore \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } < 1\qquad \qquad \qquad ...(2)$$ So from eq (1) and (2) we can say,$$\boxed { m > { m }_{ 0 } } .$$For a particle moving with 50% of the velocity of light, the mass m is 1.155mo. and when the particle is moving with 99% of the velocity of light then m = 7mo. It means as the velocity of projectile increases in the cyclotron, the mass increases and time taken by projectile is not constant. As a result the particle are not reaching at the constant time in the gap. It means the particle arrive at the gap either a little before or little after the instant at which the potential of the dees changes. The particles therefore acquire little or no additional energy. The Cyctotron therefore cannot impart energy to the projectile beyond a certain limit. In 1945, V.Veksler in the Russia and Monillan in US showed that relativistic increase in the mass can be compensated by adjusting the magnetic field. This is called the principle of phasestability. Such type of cyclotron in which this adjustment is made are known as Syachro Cyctotron In 1945, a cyclotron based on this principle was built at Berkeley, California. It has magnets with pole faces 184 inches in diameter and weighs about 4000 tons. Protons with 730 MeV energy have been produced with this synchro-cyctotron. At Batavia, Illinois in the United States is a synchrocyctotron which can impart 400 Billion electron volt (BeV).

MCQ on Nuclear Chemistry from Physical Chemistry
###### Prof. Gianfranco Coletti

Shared publicly - 2019-08-23 00:00:00

Don’t want your columns to simply stack in some grid tiers? Use a combination of different classes for each tier as needed. See the example below for a better idea of how it all works.

###### Prof. Maheshwar Sharon

Shared publicly - 2019-08-24 00:00:00

For grids that are the same from the smallest of devices to the largest, use the .col and .col-* classes. Specify a numbered class when you need a particularly sized column; otherwise, feel free to stick to

###### sunil

Shared publicly - 2023-02-28 11:09:52

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###### ss

Shared publicly - 2023-02-28 10:48:10

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