How Is Frequency Calculated in the Stern-Gerlach Experiment?

In summary, the problem involves a Stern-Gerlach experiment with a beam of silver and a magnetic moment due to the spin of the single valence electron. The goal is to compute the energy difference of the silver atoms in the two existing beams and find the frequency of the radiation that would induce a transition between these two states. The energy of each beam is calculated using the equation U=μs·B, where g≈2 and B=1. The resulting energy difference is ΔE= \hbar \frac{e}{m_e}. The second part of the problem involves finding the frequency of the radiation, but the lack of quantized energies makes it difficult to determine where to start.
  • #1
erok81
464
0

Homework Statement



I have a Stern-Gerlach experiment with a beam of silver and a magnetic moment due to the spin of the single valence electron give by μ=e/me S. And |S|=ℏ/2. The magnetic field is 1T.

The problem asks to compute the energy difference of the silver atoms in the two existing beams. The second part - which I am really confused on - Next up I am to find the frequency of the radiation that would induce a transition between these two states.

Homework Equations




The Attempt at a Solution



The energy of each beam is U=μs·B

Hence the energy is

[tex]E=\pm \frac{1}{2} \hbar \frac{e}{m_e} g B[/tex]

Therefore ΔE is

[tex]E= \frac{1}{2} \hbar \frac{e}{m_e} g B ~+~ \frac{1}{2} \hbar \frac{e}{m_e} g B~=~ \hbar \frac{e}{m_e} [/tex]

Where g≈2 and B=1 so there is a little cancelling.

My units end up being N·m = J.

I am worried this is wrong. My answer is really close to the Bohr Magneton. It is off by a 2 in the denominator and my units aren't quite right. So I guess first off, did I proceed correctly so far?

If that is correct, how does one even begin the second half? With no quantized energies I don't know where to start.
 
Physics news on Phys.org
  • #2
I'm assuming it involves the energy difference, but I'm not sure. Any help would be greatly appreciated!
 

FAQ: How Is Frequency Calculated in the Stern-Gerlach Experiment?

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 was designed to measure the magnetic moment of atoms and demonstrated the quantum nature of spin.

How does the Stern Gerlach Experiment work?

The experiment works by passing a beam of silver atoms through a strong magnetic field. The atoms align themselves either up or down based on their spin, and this causes them to be deflected in different directions. The resulting pattern on the detector plate shows the discrete quantization of spin, rather than a continuous range of values.

What were the results of the Stern Gerlach Experiment?

The results of the experiment showed that the angular momentum of an atom is quantized, meaning it can only take on certain discrete values. This discovery was a crucial step in the development of quantum mechanics and helped to confirm the wave-particle duality of matter.

What impact did the Stern Gerlach Experiment have on modern physics?

The Stern Gerlach Experiment had a significant impact on modern physics. It provided evidence for the quantization of angular momentum and the discrete nature of spin, which led to the development of quantum mechanics. It also paved the way for future experiments and research in quantum mechanics and atomic physics.

Are there any applications of the Stern Gerlach Experiment?

Yes, there are several applications of the Stern Gerlach Experiment. It has been used to study the properties of atoms, molecules, and subatomic particles. It has also been used in the development of technologies such as magnetic resonance imaging (MRI) and quantum computing. Additionally, the principles of the experiment have been applied in various fields, including chemistry, biology, and materials science.

Similar threads

Stern-Gerlach: Measurements of spin
Replies
16
Views
2K
Determine Field Gradient of a Stern Gerlach Magnet....
Replies
3
Views
2K
A Quantitative description of successive Stern-Gerlach measurements
Replies
1
Views
987
I Do physically rotating particles affect Stern Gerlach results?
Replies
16
Views
416
I When was the formula for the Stern-Gerlach experiment found?
Replies
7
Views
1K
I Problem involving a sequential Stern-Gerlach experiment
Replies
24
Views
3K
I Question about Stern-Gerlach experiment
Replies
12
Views
2K
I Is Stern-Gerlach experiment a proper idealization of measurnment?
Replies
12
Views
2K
I How many spots will a rotating Stern-Gerlach apparatus produce?
Replies
32
Views
1K
I Who was the first to make a Stern-Gerlach experiment with two magnets?
Replies
9
Views
1K

Hot Threads

Recent Insights

Back
Top