each element has a different has a different set of energy level use this fact to explain why colour of light emited by an element in gaseous state is the characteristics of the element

The light emitted is characteristic of a specific set of allowed quantum levels, each element has its own individual ground states.

thanks Bob I understand the question now

how do i find the energy levels of mercury?

Great! Let me further explain how the color of light emitted by an element in its gaseous state is related to its energy levels.

When an element is in its gaseous state and is excited (for example, by heating or sending an electric current through it), its electrons absorb energy and move to higher energy levels or orbitals. These excited electrons are in what is known as an "excited state."

However, electrons cannot remain in these excited states indefinitely. They tend to return to their lower energy levels or ground state. As they do so, they release the excess energy they gained in the form of light, specifically in the visible range of the electromagnetic spectrum.

Now here comes the interesting part. The energy levels or orbitals that electrons transition between in an atom are unique to each element. Each element has a specific arrangement of electrons and a distinct set of allowed energy states. This means that the energy absorbed and emitted by an element will be different from that of other elements.

The energy released by electrons as they move from higher to lower energy levels corresponds to specific wavelengths of light. And as we know from the study of optics, different wavelengths of light correspond to different colors. So, when the electrons of an element return to their ground state and emit light, the color of that light will be unique to the element.

Scientists can observe the emitted light, disperse it using a prism or spectrograph, and analyze the resulting spectrum of colors. By comparing this spectrum with known spectra of elements, they can identify which element has emitted the light based on its characteristic color or combination of colors.

In summary, the color of light emitted by an element in its gaseous state is a result of the specific energy levels and transitions unique to that element, making it a characteristic feature for identification.