(Hmpf I was almost finished when John Rennie posted his anwer .... you can see it as a supplement.)

What generates absorption and emission lines are the differences in energy levels. As an example take sodium: when you heat the sodium vapor you push electrons in excited energy states, when those electrons jump from the excited in the ground state they emit photons with a specific energy. What you then see are emission lines, in the image below this is the part on the top.

On the other hand you could send white light (composed of all wavelengths) through a non-heated sodium vapor. In this vapor photons with a certain frequency,i.e. energy, push electrons from the ground in the excited state. In this case you see absorption lines, in the picture below this is the part on the bottom.

So the photons emitted make emission lines and the photons which are absorbed are responsible for absorption lines.

The same principle takes place with the hyperfine transition: you have two states with different energies. When the electrons jumps from the higher (spin up) state to the lower (spin down) it emits a photon and conversely it has to absorb a photon if it wants to jump from the lower to the higher state.

So the energy is in both cases the same, but one time the photon is absorbed and the other time it is emitted.

Yes the spectral lines have a frequency. Either you measure the frequency directly or you measure the wavelength of the photons. When you know the wavelength you can calculate the frequency via $$\lambda f = c, $$ where $\lambda$ is the wavelength and $c$ is the speed of light. (Indeed, when you put the two numbers from the Wikipedia article in you get this result.) This in turn gives you the energy the photons have and consequently the difference of the two energy levels: $$E=\hbar f. $$

(Hmpf I was almost finished when John Rennie posted his anwer .... you can see it as a supplement.)

What generates absorption and emission lines are the differences in energy levels. As an example take sodium: when you heat the sodium vapor you push electrons in excited energy states, when those electrons jump from the excited in the ground state they emit photons with a specific energy. What you then see are emission lines, in the image below this is the part on the top.

On the other hand you could send white light (composed of all wavelengths) through a non-heated sodium vapor. In this vapor photons with a certain frequency,i.e. energy, push electrons from the ground in the excited state. In this case you see absorption lines, in the picture below this is the part on the bottom.

So the photons emitted make emission lines and the photons which are absorbed are responsible for absorption lines.

The same principle takes place with the hyperfine transition: you have two states with different energies. When the electrons jumps from the higher (spin up) state to the lower (spin down) it emits a photon and conversely it has to absorb a photon if it wants to jump from the lower to the higher state.

So the energy is in both cases the same, but one time the photon is absorbed and the other time it is emitted.

Yes the spectral lines have a frequency. Either you measure the frequency directly or you measure the wavelength of the photons. When you know the wavelength you can calculate the frequency via $$\lambda f = c, $$ where $\lambda$ is the wavelength and $c$ is the speed of light. (Indeed, when you put the two numbers from the Wikipedia article in you get this result.) This in turn gives you the energy the photons have and consequently the difference of the two energy levels: $$E=\hbar\omega\quad\text{with}\;\omega=2\pi f $$