The ratio of de - Broglie wavelength of `alpha `- particle to that of a proton being subjected to the same magnetic field so that the radii of their path are equal to each other assuming the field induction vector `vec(B)` is perpendicular to the velocity vectors of the `alpha` - particle and the proton is
A
1
B
`(1)/(4)`
C
`(1)/(2)`
D
2
Text Solution
Verified by Experts
The correct Answer is:
C
When a charged particle of charge q , mass m enters perpendicularly to the magnetic induction `vec B` of a magnetic field, it will experience a magnetic force `F= q (vec v xx vec B) =qvBsin 90^(@)`=qvB that provide a cetripetal acceleration `(v^(2))/(r)` , `implies qv B= (mv^(2))/(r) implies mv=qBr`, `implies` The de -Broglies wavelength `lambda=(h)/(wv)=(h)/(qBr)`, `implies (`lambda_(alpha-particle))/(lambda_(proton))=(q _(p) r_(p))/(q _(alpha) r_(alpha))` Since `(r_(alpha))/(r_(p))`=1 and `(q_(alpha))/(q_(p))=2 `, `implies =(1)/(2)`
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