Velocity filter is an arrangement of cross electric and magnetic fields in a region which helps us to select form a beam charged particles of the given velocity irrespective of their charge and mass.
A velocity selector consists of two slits S1 and S2 held parallel to each other with common axis some distance apart. In the region between the slits uniform electric and magnetic fields are applied perpendicular to each other as well as to the axis of slits when a beam of charged particles of different charges and masses after passing through slit S1 enters the region of crossed electric field E and magnetic field B each particle experiences a force due to these fields those particles which are moving with the velocity v irrespective of their mass and charge if force on each such particle due to electric field (qE) is equal and opposite to the force due to magnetic field (q v B ) then
qE = q v B or v = E / B
Such particles will go undedicated and filtered out of the region through the slit S2 therefore; the particles emerging from slit S2 will have the same velocity even though their charge and mass may be different.
The velocity filter is used in mass spectrograph which helps to find the mass and specific charge (charge/mass) of the charged particle.
Mass spectrograph is an apparatus used to determine mass or specific charge (charge/mass) of charge particles. A Bain bridge mass spectrograph is shown is A fine beam of positively charged ions after passing through slit S1 enters a region of crossed electric and magnetic fields acting as velocity selector. The charged ions emerging through the velocity selector will have the same velocity v = E/B these ions are collimated by slit S2 and them subjected to a uniform perpendicular magnetic field B acting inwards. The positive ions having same charge but different masses will describe the circular path of different radii in the magnetic field and finally they reach on the photographic plate P at different locations.
If r is the radius of the circular path of an icon, having charge q and mass m then mv2/r = q v B or q / m = v / rB =E / r B, B
It means; q / m ∝ 1 / r or m ∝ r (if q is same for all ions)
This shows that the lighter ions will describe the circular path of smaller radius while reaching the photographic plate and heavier ions will describe the circular path of greater radius while reaching the photographic plate.
On the photographic plate the different spots will indicate the ions of different masses but having same charge knowing the relative separation between the spots on screen the number of isotopes present and their specific charge can be estimated.
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