Question

A deuteron and an alpha particle having same momentum are in turn allowed to pass through a magnetic field B→, acting normal to the direction of motion of the particles. Calculate the ratio of the radii of the circular paths described by them ??​

Answer 1

Answer:

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Explanation:

Mass of deuteron = 2 units= md

Charge on deuteron = 1 unit = qd

Mass of alpha particle = 4 units = mα

Charge on alpha particle = 2 units = qα

Radius of circular path R=mvqB

Radius of deuteronRadius of alpha particle=RdRα⇒mdvdqd·B·qα·Bmαvα

Since the momentum of the alpha particle and deuteron are same.

∴ md .vd = mα .vα

⇒RdRα=md·vd·qα·Bqd·B·mα·vα=qαqd=21=2

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Answer 2

Mass of deuteron = 2 units= md

Charge on deuteron = 1 unit = qd

Mass of alpha particle = 4 units = mα

Charge on alpha particle = 2 units = qα

Radius of circular path R=mvqB

Radius of deuteronRadius of alpha particle=RdRα⇒mdvdqd·B·qα·Bmαvα

∵the momentum of the alpha particle and deuteron are same.

∴ md .vd = mα .vα

⇒RdRα=md·vd·qα·Bqd·B·mα·vα=qαqd=21=2