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polet [3.4K]
3 years ago
9

A proton (mass mp), a deuteron (m = 2mp, Q = e), and an alpha particle (m = 4mp, Q = 2e), are accelerated by the same potential

difference V and then enter a uniform magnetic field B where they move in circular paths perpendicular to B. Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton.
Physics
1 answer:
allsm [11]3 years ago
7 0

Answer with Explanation:

We are given that

Mass of deuteron=2m_p

Charge, Q=e

Mass of alpha particle=4m_p

Charge,q=2e

Magnetic field=B

Mass of proton=m_p

Let radius of path of proton=r

v=\sqrt{\frac{2qV}{m}}

Using the formula

Velocity of proton=v=\sqrt{\frac{2qV}{m}}

Centripetal force =Magnetic force

\frac{mv^2}{r}=qvB

r=\frac{mv}{qB}

Radius of proton,r=\frac{m_p\times\sqrt{\frac{2eV}{m_p}}}{eB}=\frac{\sqrt{2V}}{B}\sqrt{\frac{m_p}{e}}

Radius of deuteron,R=\frac{\sqrt{2V}}{B}\times \sqrt{\frac{2m_p}{e}}

\frac{R}{r}=\sqrt{2}

R=\sqrt{2}r

Radius of alpha particle,R'=\frac{\sqrt{2V}}{B}\times\sqrt{\frac{4m_p}{2e}}

\frac{R'}{r}=\sqrt 2

R'=\sqrt{2} r

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