Field gradient in a 50-cm Stern-Gerlach magnet for silver atoms

[grandpa2390]

Homework Statement

Here is the Problem. I have the Solution but am having trouble understanding parts of it.

1.1. Determine the field gradient of a 50-em-long Stem-Gerlach magnet that would produce a 1-mm separation at the detector between spin-up and spin-down silver atoms that are emitted from an oven at T = 1500 K. Assume the detector (see Fig. 1.1) is located 50 em from the magnet. Note: While the atoms in the oven have average kinetic energy 3kBT j2, the more energetic atoms strike the hole in the oven more frequently. Thus the emitted atoms have average kinetic energy 2kBT, where kB is the Boltzmann constant. The magnetic dipole moment of the silver atom is due to the intrinsic spin of the single electron. Appendix F gives the numerical value of the Bohr magneton, in a convenient form.

Homework Equations

Kinematic Equations

The Attempt at a Solution

The one part I don't understand is this:

I get that the units work out. But I don't understand why the formula is in this way. particularly the second term that isn't 1/2at^2 but a*t1*t2

 

[TSny]

Can you interpret the quantity $a_z \left(\frac{l_1}{v} \right) = a_z t_1$?

 

[grandpa2390]

Can you interpret the quantity $a_z \left(\frac{l_1}{v} \right) = a_z t_1$?

As always. I stood stumped about the question for days. when I finally ask for help, it clicks.

the first term is the distance traveled up in the magnets.
the second term is the distance traveled up outside the magnets. there is no acceleration it is just vt where v is the velocity after leaving the magnet and t is the time spent outside of the magnet. : )

 

[TSny]

Yes. Good.