91影视

In the Stern-Gerlach experiment for neutral silver atoms, the magnetic field has magnitude,$\left|\stackrel{鈫�}{\mathrm{B}}\right|=0.50\mathrm{T}$

The Stern-Gerlach experiment revealed that angular momentum's spatial direction may be quantized.

Using the concept of energy difference derived from the experiment, the required value of the energy. Using this energy, the frequency of electromagnetic radiation. Now, using this frequency, the wavelength of the radiation. This determines the wave region in the electromagnetic spectrum. The wave region of a short radio wave ranges from a few thousand meters to 30 cm .

Formulas:

The energy equation from the Stern-Gerlach experiment,

$鈭�\mathrm{E}=2{\mathrm{渭}}_{\mathrm{B}}\mathrm{B}$ 鈥�.. (1)

Here, The Bohr magneton${\mathrm{渭}}_{\mathrm{B}}=9.27脳{10}^{-24}\mathrm{J}/\mathrm{T}$

The energy due to Planck-Einstein relation is,

$鈭�\mathrm{E}=\mathrm{hf}$ 鈥�.. (2)

Here, the Plank鈥檚 constant is

The wavelength of wave radiation is,

鈥�.. (3)

Here, the speed of light is .

Using the given values in equation (1), the energy difference between the magnetic moment orientations of the silver atoms in the two sub-beams (in terms of eV ) as follow.

$$\begin{gathered} 鈭�\mathrm{E}=\frac{2\left(9.27脳{10}^{-24}\mathrm{J}/\mathrm{T}\right)\left(0.50\mathrm{T}\right)}{\left(1.6脳{10}^{-19}\mathrm{J}/\mathrm{eV}\right)} \\ =58\mathrm{渭别痴} \end{gathered}$$

Hence, the value of the energy difference is $58\mathrm{渭别痴}$.

Now, substituting the above energy difference value in equation (2), the frequency of the electromagnetic radiation as follows:

$$\begin{gathered} \mathrm{f}=\frac{鈭�\mathrm{E}}{\mathrm{h}} \\ =\frac{\left(58\mathrm{渭别痴}\right)\left(1.6脳{10}^{-19}\mathrm{J}/\mathrm{eV}\right)}{6.63脳{10}^{-34}\mathrm{J}.\mathrm{s}} \\ =1.4脳{10}^{10}\mathrm{Hz} \\ =14\mathrm{GHz} \end{gathered}$$

Hence, the value of the frequency is 14 GHz.

Using the above frequency value in equation (3), the wavelength of the radiation as follow.

$$\begin{gathered} \mathrm{位}=\frac{3脳{10}^8\mathrm{m}/\mathrm{s}}{14脳{10}^9\mathrm{Hz}} \\ =2.1\mathrm{cm} \end{gathered}$$

Hence, the value of the wavelength is 2.1 cm .

The wavelength of this radiation lies in the region of the shortwave radio waves.

Hence, the electromagnetic spectrum is for a short radio wave.