Home
Class 12
PHYSICS
Find the ratio of de Broglie wavelength ...

Find the ratio of de Broglie wavelength of an `alpha`-particle to that of a photon being subjected to the same magnetic field so that the radii of their path are equal to each other assuming the field induction vector `vecB` is perpendicular to the velocity vectors of the `alpha`-particle and proton.

A

`1`

B

`1//4`

C

`1//2`

D

`2`

Text Solution

Verified by Experts

When a charged particle of charge `q`, mass `m` enters perpendicularly to the magnetic induction `vecB` of a magnetic field, it will experience a magnetic force `F=q(vecvxxvecB)=q vB sin 90^(@)=qvB` that provide a centripetal acceleration `(v^(2))/(r )`
`rArr qvB=(mv^(2))/(r )rArrmv=qBr`
`rArr` The `de`-Broglie wavelength `lambda=(h)/(mv)=(h)/(qBr)`
`rArr (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`
`rArr (lambda_(alpha))/(lambda_(p))=1//2`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

What will be the ratio of de - Broglie wavelengths of proton and alpha - particle of same energy ?

Find the ratio of de Broglie wavelength of an alpha -particle and a deutron if they are accelerating through the same potential difference

The ratio of the de Broglie wavelength of a proton and alpha particles will be 1:2 if their

The ratio of the de Broglie wavelength of a proton and alpha particles will be 1:2 if their

Find the ratio of de Broglie wavelength of a proton and as alpha -particle which have been accelerated through same potential difference.

Ionized hydrogen atoms and alpha- particle with moments enters perpendicular to a constant megnetic field. B. The ratio of their radii of their paths r_(H): r_(alpha) be :

A stream of protons and alpha -particle of equal momenta enter a unifom magnetic field perpendicularly. The radii of their orbits are in the ratio

A proton and an alpha -particles enters in a uniform magnetic field with same velocity, then ratio of the radii of path describe by them

A proton and an alpha particle projected with same velocity in uniform transverse magnetic field then