why a particular element should have unique emission spectrum?

Each element has a series of 'shells' that contain the the electrons. These shells are all approximately in the same place. The emission spectrum is when an electron moves from a higher orbital to a lower one and in doing so releases a quanta of energy.

Although the movement is basically the same, the energy for each transition is different depending on the attractive forces between the electron and the nucleus.

Take your example. A transition between two shells of say He and Li+. Both have the same number of electrons and the electron in question is moving between the same shells. The difference is that the He has 2 protons to attract whereas the Li+ has three to that the quanta required are different hence you get a different wavelength and different spectra.

EDIT: Another example. Take the end of a rubber band and nail it to a board. Take the other end and without stretching it mark the point were it extends to. Now stretch the rubber band 5 cm. It takes a certain amount of force to do so.

Now do the same thing with 2 rubber bands. You have moved the band through the same distance but it has taken a substantial amount of extra energy.

Think of the nailed end being the nucleus, the number of rubber bands being the protons and the point being an electron. The more protons (rubber bands) you have the harder it is for the rubber band (the electron) to be extended.

--

regards

Ramesh

The emission spectrum of a chemical element or chemical compound is the relative intensity of each frequency of electromagnetic radiation emitted  by the element's atoms or the compound's molecules when they are returned to a ground state. The energy levels in atoms and ions are the key to the production and detection of light. Energy levels or "shells"exist for electrons in atoms and molecules. The colors of dyes and other compounds results from electron jumps between these shells or levels. The colors of fireworks result from jumps of electrons from one shell to another. Observations of light emitted by the elements is also evidence for the existence of shells, subshsells and energy levels. The kinds of light that interact with atoms indicate the energy differences between shells and energy levels in the quantum theory model of the atom. Typically the valence electrons are the ones involved in these jumps.

The "quantum" theory was proposed more than 90 years ago, and has been confirmed by thousands of experiments. Science and education has failed to clearly describe the energy level concept to almost four generations of citizens. This experiment is an exercise aimed at throwing a little more light on the subject. ( Don't laugh too hard at the joke.)

Atoms have two kinds of states; a ground state and an excited state. The ground state is the state in which the electrons in the atom are in their lowest energy levels possible (atoms naturally are in the ground state). This means the electrons have the lowest possible values for "n" the principal quantum number.

Specific quantized amounts of energy are needed to excite an electron in an atom and produce an excited state. The animation shows the opposite of excitation. It shows how the excited hydrogen atom with an electron in the n = 3 shell can release energy. If the electron in hydrogen only drops to the n = 2 shell the energy matches a pulse of red light.

Note the size of the electron cloud in the excited atom changes when the electron moves from shell to shell. The size of the atom decreases in volume when the electron goes from the n=3 shell to the n = 2 shell. On average the electrons are closer to the nucleus for lower values of "n". The electron cloud is related to the most probable distance between the nucleus and the electron. The most probable distance increases with increasing "n" value. The excited electron is still "in" the atom even in an excited state. The valence electron will only escape the atom if the electron is given an amount of energy equal to the ionization energy for that atom