91Ó°ÊÓ

1. The wavelength associated with that photon,$\mathrm{λ}=0.21m$
2. If the electron is excited to a higher level, it can de-excite by spin-flipping and emitting a photon.

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

The power of attraction among all the crowds throughout the universe; especially the attraction of the gravity of the earth with the bodies near its surface.

Use the concept of gravitational force to find gravitational potential energy. Integrate the equation of gravitational force over infinity to reference position. Then define the work required to increase the separation of the particles forthegiven positions.

Formulas:

The energy equation from the Stern-Gerlach experiment,

$∆\mathrm{E}=2{\mathrm{μ}}_{\mathrm{B}}\mathrm{B}$ ….. (1)

Here, B is the magnetic field and ${\mathrm{μ}}_{\mathrm{B}}$is the Bohr magneton.

The energy due to Planck-Einstein relation,

$∆\mathrm{E}=\frac{\mathrm{hc}}{\mathrm{λ}}$ ….. (2)

Here, c is the speed of light, $\mathrm{λ}$ is the wavelength, and h is the Plank’s constant.

Consider the known data as below.

The wavelength, $\mathrm{λ}=21\mathrm{cm}=0.21\mathrm{m}$

Plank’s constant, $\mathrm{h}=6.63×{10}^{-34}\mathrm{J}.\mathrm{s}$

Speed of light, $\mathrm{c}=3×{10}^8\mathrm{m}/\mathrm{s}$

Bohr magneton, ${\mathrm{μ}}_{\mathrm{B}}=9.27×{10}^{-24}\mathrm{J}/\mathrm{T}$

Comparing equations (1) and (2) and substituting the given data in the derived equation of the magnetic field.

The value of the effective magnetic field is as follow.

$$\begin{gathered} 2{\mathrm{μ}}_{\mathrm{B}}\mathrm{B}=\frac{\mathrm{hc}}{\mathrm{λ}} \\ \mathrm{B}=\frac{\mathrm{hc}}{\mathrm{λ}\left(2{\mathrm{μ}}_{\mathrm{B}}\right)} \end{gathered}$$

Substitute known values in the above equation.

$$\begin{gathered} \mathrm{B}=\frac{\left(6.63×{10}^{-34}\mathrm{J}.\mathrm{s}\right)\left(3×{10}^8\mathrm{m}/\mathrm{s}\right)}{2\left(0.21\mathrm{m}\right)\left(9.27×{10}^{-24}\mathrm{J}/\mathrm{T}\right)} \\ =5.11×{10}^{-2}\mathrm{T} \\ =51\mathrm{mT} \end{gathered}$$

Hence, the value of the magnetic field is 51 mT.