Question

A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is ______.

Options

• 1 : `sqrt2:sqrt2`  

• 1 : 1 :`sqrt2`  

• `sqrt2` : 1 : 1

• 1 : `sqrt2` : 1  

Answer 1

A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is 1 : `sqrt2` : 1.

Explanation:

Radius of circular path in uniform magnetic field is given by, r = `"mV"/"qB"`

= `sqrt((2"m"("K"."E".))/"qB")`

As K.E = constant

So, r ∝ `sqrt("m"/"q")`

So, r_p : r_d : r_α = `sqrt"m"/"e": sqrt(2"m")/"e":sqrt(4"m")/(2"e")`

= 1 : `sqrt2` : 1