Question

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let `r_d` and `r_alpha` be their respective radii of the circular path. The value of `(r_d)/(r_alpha)` is equal to ______.

Options

• `sqrt2`

• 1

• 2

• `1/sqrt2`

Answer 1

A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let `r_d` and `r_alpha` be their respective radii of the circular path. The value of `(r_d)/(r_alpha)` is equal to `bbunderline(sqrt2)`.

Explanation:

Making use of the expression,

`r = (mv)/(qB) = sqrt(2mK)/(qB)`

Because the kinetic energy of the deuteron and the alpha particle is the same,

`K_d = K_alpha` .....(given)

`(r_d)/(r_alpha) = sqrt(m_d/m_alpha)(q_alpha)/(q_d)`

⇒ `(r_d)/(r_alpha) = sqrt(2/4) (2/1) = sqrt2`