Can you tell me more about the experiments showing that different elements made different spectral lines?

Spectral lines were first seen in the sun's spectrum by William Wollaston in 1802. However, they were not systematically studied until 1814, when a German optician named Joseph von Fraunhofer observed and catalogued them. Fraunhofer carefully recorded the positions of the lines, but he didn't attempt to explain why they were there. In the late 1850's, the physicist Gustav Kirchhoff decided to investigate further, with the help of the chemist Robert Bunsen.

Did he invent the Bunsen burner?

Yes, and that's what Bunsen and Kirchhoff used to perform their experiments. They held crystals of various substances in the flame from a Bunsen burner; the crystals would then glow with particular colors, and, with a prism, the light from them could be separated into spectra like the ones you saw.

And they found that each element had its own unique set of lines?

They certainly did. A given element would always produce the same spectrum, which was different from that of any other element. In fact, in the 1860's, Kirchhoff and Bunsen discovered two new elements, cesium and rubidium, when they came across some spectral lines that didn't fit any of the known elements. Later, the elements of gallium, helium, argon, neon, krypton, and xenon were also discovered using spectroscopy.