Notes: Mass spectrometer
- Velocity selector + uniform B field
- Charges are emitted to the right, into the uniform B field region.
Equations
- Velocity selector → v = E / B
- Motion through uniform B → m v = q B r
- Together, m/q = B2 / E × r
- We can easily control B and E, and measure r.
- → now we have access to determining m/q for charged particles.
Electrons
- Send electrons through → Single semicircle.
- Things we can prove: stream is made of a single type of particle (single circle), B = in and circle is CW → particles have negative charge
- If we make B = 0.00020 T, E = 100 N/C, r = 0.014 m, and we are able to independently measure q = -1.6×10-19, we have determined the mass of electrons.
Hydrogen
- Send ionized hydrogen gas through → Two semicircles.
- Things we can prove: stream is made of a single type of particle (single circle), B = in and circles are CCW → particles have positive charge
- If we measure that they both have the same charge, and 1 circle is twice the size of the other, we have shown that there are two particles, one with twice the mass of the other.
- Note: larger circles (Deuterium) is MUCH less intense than smaller. 1H is much more abundant.
Example: Mass spectrometer
- An unknown sample of material is analyzed with a mass spectrometer.
- When electric field has intensity 6000 N/C and magnetic field has intensity 0.050 T, particles hit 0.234 m from selector.
- If we also know that the particles are triply ionized, what are they most likely to be?
Solution
- 2: Diagram
- 3: E = 6000 N/C, B = 0.050 T, r = 0.117 m, q = 4.8×10-19 C, looking for m
- 4: Mass spectrometer
- 5: m/q = B2 r / E
- 6: no simplifications.
- 7: m = 2.34×10-26kg = 14.1 amu.
- 8: atoms with atomic mass 14: 14C, and 14N. Much more likely to be 14N.
- Note: 1.66×10-27kg = 1 amu
Example: Hall effect
- A conductor carries current to the right.
- The conductor is in a uniform B field, upwards.
+ charge carriers
- v is to right
- qv is to right
- RHR 1 → F is out.
- + accumulates on near side, leaving - on far side, ΔV (front - back) is positive
- charge carriers
- v is to LEFT
- qv is to right
- RHR 1 → F is out.
- - accumulates on near side, leaving + on far side, ΔV (front - back) is negative
Observation
- ΔV is measured to be negative for metal
- → charge carrier in metals is negative
- → evidence that current is due to traveling electrons.