Question

Various singly-ionized atomic nuclei of the same speed are directed into a magnetic field in a mass spectrometerwhere they are deflected and strike a detecting screen. The particles most strongly deflected are those ofa) least mass b) greatest mass c) same for all

Answer 1

Answer:

a) least mass

Explanation:

According to the Newton's first law of motion, more the mass of a body the greater is its inertia, and inertia is the tendency of a body to resist any change to its state of rest or uniform motion.

Greater is the mass of charge least is its deflection under the influence of magnetic field.

This can be explained well by the mathematical equations relating the centripetal force and the magnetic force on a charged mass moving in a magnetic field perpendicular to the velocity:

$m.\frac{v^2}{r} =q.v.B$

where:

m = mass of the charged particle

v = velocity of projection of the charged mass into the magnetic field

r = radius of curvature of path of charged mass under the magnetic force

q = magnitude of charge on the particle of mass 'm'

B = intensity of magnetic field normal to 'v'

$\Rightarrow v=\frac{q.B.r}{m}$

$\Rightarrow v\propto \frac{1}{m}$

i.e.

• Speed of the charge is higher when its mass is lesser and according to the Fleming's left hand rule we known that the charge continuously faces a magnetic force while moving in the field.

& also,

$\Rightarrow m\propto \frac{1}{r}$

• Which indicates that more is the mass of charge larger is the radius of its trajectory of motion which means lesser is its deviation.