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A proton, an electron and a Helium nucleus have the same kinetic energy. They are in circular orbits in a plane due to a magnetic field which is perpendicular to the plane. Let r p , r e and r H e be their respective radii, then

Options

  1. Ar e > r p = r H e
  2. Br e > r p > r H e
  3. Cr e < r p < r H e
  4. Dr e < r p = r H e

Correct answer

D. r e < r p = r H e

Step-by-step solution

Radius of circle is given by r = m v q B = p q B = 2 m K q B = 2 m q B K (where K is kinetic energy) For proton, r p = 2 m p e B K For electron, r e = 2 m e e B K For H e 2 + , &#160; r H e = 2 &#215; 4 m p 2 e B K = 2 m p e B K Clearly, r H e = r p &#62; r e

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