91影视

Wavelengths of the two closely spaced lines are ${\mathrm{位}}_1=588.995\mathrm{nm}\mathrm{and}{\mathrm{位}}_2=589.592\mathrm{nm}$.

The given state, n = 3, I = 1

Magnetic resonance, absorption or radiation by electrons or atomic nuclei in response to the use of other magnetic fields.

Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the magnetic frequency of the photon and thus, equally, equates to the wavelength of the wave. When the frequency of photons is high, its potential is high.

For the given closely spaced lines, the value of the energy difference between the two lines can be given using Planck's relation and the given data. Again, for the energy difference, there exists a magnetic field due to the resonance between them; this is calculated using the energy equation from the Stern-Gerlach experiment.

Formulas:

The energy of the photon due to Planck鈥檚 relation,

$鈭�\mathrm{E}=\frac{\mathrm{hc}}{\mathrm{位}}$ 鈥�.. (1)

Here, consider the known data below.

The Plank鈥檚 constant is,

$$\begin{gathered} \mathrm{h}=6.63脳{10}^{-34}\mathrm{J}.\mathrm{s} \\ =\left(6.242脳{10}^{18}脳6.63脳{10}^{-34}\right)\mathrm{eV}.\mathrm{s} \\ =41.384脳{10}^{-16}\mathrm{eV}.\mathrm{s} \\ \mathrm{The}\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{is}, \\ \mathrm{c}=3脳{10}^8\mathrm{m}/\mathrm{s} \\ =\left(3脳{10}^8脳{10}^9\right)\mathrm{nm}/\mathrm{s} \\ =3脳{10}^{17}\mathrm{nm}/\mathrm{s} \end{gathered}$$

The energy difference between two closely spaced lines from the Stern-Gerlach experiment is,

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

Here, the Bohr magneton is,

${\mathrm{渭}}_{\mathrm{B}}=5.788脳{10}^{-5}\mathrm{eV}/\mathrm{T}$

Using the given data in equation (1), the energy difference between the two upper levels of the lines can be calculated is as follows.

$$\begin{gathered} 鈭�\mathrm{E}=\frac{\mathrm{hc}}{{\mathrm{位}}_1}-\frac{\mathrm{hc}}{{\mathrm{位}}_2} \\ =\mathrm{hc}\left[\frac{1}{{\mathrm{位}}_1}-\frac{1}{{\mathrm{位}}_2}\right] \end{gathered}$$

Substitute known values in the above equation.

$$\begin{gathered} 鈭�\mathrm{E}=\left(41.384脳{10}^{-16}\mathrm{eV}.\mathrm{s}\right)\left(3脳{10}^{17}\mathrm{nm}/\mathrm{s}\right)\left[\frac{1}{588.995\mathrm{nm}}-\frac{1}{589.592\mathrm{nm}}\right] \\ =1240\mathrm{eV}.\mathrm{nm}\left[\frac{0.0016978}{\mathrm{nm}}-\frac{0.0016961}{\mathrm{nm}}\right] \\ =1240\mathrm{eV}.\mathrm{nm}\left[\frac{1.7脳{10}^{-6}}{\mathrm{nm}}\right] \\ =2.11\mathrm{meV} \end{gathered}$$

Hence, the value of the energy difference is 2.11 meV.

Using the above value in equation (2), the magnitude of the given internal magnetic field can be calculated as follows:

$$\begin{gathered} \mathrm{B}=\frac{鈭�\mathrm{E}}{2{\mathrm{渭}}_{\mathrm{B}}} \\ =\frac{2.11脳{10}^{-3}\mathrm{eV}}{2\left(5.788脳{10}^{-5}\mathrm{eV}/\mathrm{T}\right)} \\ =18\mathrm{T} \end{gathered}$$

Hence, the value of the magnetic field is 18 T.