Stern-Gerlack Experiment with silver atoms

In summary, the Stern-Gerlach experiment involves a magnet with a varying magnetic field along the vertical direction, causing a separation of two silver atom beams. The magnetic field increases by 26.00 T per centimeter, with a horizontal length of 7.1 cm. The speed of the silver atoms is 922 m/s and the mass is 1.800×10-25 kg. To find the separation of the beams, the equations used are F = -2600, Fz = -μB(2600), and θ = tan^-1(μB). However, this solution does not fully account for the multiple angular momentum states involved.
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Homework Statement



The magnetic field in a Stern-Gerlach experiment varies along the vertical direction so that the magnetic field increases by 26.00 T each centimeter. The horizontal length of the magnet is 7.1 cm, and the speed of the silver atoms is 922 m/s. The mass of the silver atom is 1.800×10-25 kg. What is the separation of the two silver atom beams as they leave the magnet?

Homework Equations



[itex] F = - \nabla V [/itex]

[itex] F_{z} = - m_{l} \mu_{B} \frac{dB_z}{dz} [/itex]

[itex] B = 2600 z [/itex]

where z is the vertical position

The Attempt at a Solution



I started out thinking I was looking for an angle between the two paths, so I found

F = -2600

and [itex] F_z = - \mu_B (2600) [/itex]

solving for theta:

[itex]\theta = tan^{-1}(\frac{-2600\mu_{B}}{-2600})[/itex]

which simplifies to [itex] tan^{-1}(\mu_B)[/itex]

and that doesn't sit well with me.

Any ideas?
 
Last edited:
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and that doesn't sit well with me.
why not?

why do you have a F as well as Fz?
how did you use the length of the magnet and the speed of the atoms?
did you take into account that there is more than one angular momentum state involved?

note:
##F_z = m_{Ag}a_z## isn't it?
 

1. What is the Stern-Gerlach experiment?

The Stern-Gerlach experiment is a physics experiment that was conducted in 1922 by Otto Stern and Walther Gerlach. It is a landmark experiment that demonstrated the quantization of angular momentum and the concept of spin in quantum mechanics.

2. How does the Stern-Gerlach experiment work?

The experiment involves sending a beam of neutral silver atoms through an inhomogeneous magnetic field. The atoms are deflected by the magnetic field according to their spin orientation, with atoms having a spin aligned with the field being deflected one way and atoms with opposite spin being deflected in the opposite direction. This creates a pattern on the detection screen, showing that the atoms have discrete spin values rather than a continuous range of values.

3. What were the results of the Stern-Gerlach experiment?

The results of the experiment showed that the silver atoms had two discrete spin states, rather than a continuous range of values. This demonstrated the quantization of angular momentum and the concept of spin in quantum mechanics. It also provided evidence for the existence of intrinsic angular momentum in particles, which was later named spin.

4. Why is the Stern-Gerlach experiment important?

The Stern-Gerlach experiment is important because it provided strong evidence for the existence of spin in particles and helped to confirm the principles of quantum mechanics. It also paved the way for further research and experiments in quantum mechanics, leading to significant advancements in our understanding of the subatomic world.

5. How has the Stern-Gerlach experiment impacted modern science?

The Stern-Gerlach experiment has had a significant impact on modern science, particularly in the field of quantum mechanics. It provided key insights into the nature of particles and their intrinsic properties, leading to the development of new theories and technologies. It also helped to shape our understanding of the fundamental laws of nature and has had numerous applications in fields such as quantum computing and information processing.

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