a proton, a deuteron and an a-particle are moving with same momentum in a uniform magnetic field. find ratio of their time period

Sagot :

The ratio of their time period is 1 : 2 : 2.

The momentum of a proton, a deuteron, and an alpha particle is the same in a uniform magnetic field.

The charge of a proton is q = e and the let m(p) be the mass of the proton.

Let m(d) = 2m(p) be the mass of the deuteron and the charge of a deuteron is q =e.

Now, an alpha particle is made up of 4 protons. Therefore the mass of an alpha particle is 4m(p) and the charge on an alpha particle is q = 2e.

The formula for the time period of a moving particle in a uniform magnetic field is given as:

[tex]T = \frac2 \pi m}{qB}[/tex] where B is the magnetic field, m is the mass and q is the charge of the particle.

So, the time period of a proton is:

[tex]T_{1} = \frac{2 \pi m(p)}{eB}[/tex]

The time period of a deuteron is:

[tex]T_{2} = \frac{2 \pi (2m(p))}{eB}[/tex]

And the time period of an alpha particle is:

[tex]T_{3} = \frac{2 \pi ( 4m(p) )}{2eB}[/tex]

Therefore, the ratio is:

[tex]T_{1}: T_{2} : T_{3} =\frac{2 \pi m(p)}{eB} : \frac{2 \pi 2m(p)}{eB} : \frac{2 \pi (4m(p))}{2eB}[/tex]

T₁ : T₂ : T₃ =  1 : 2 : 2

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