A spectrometer is used to analyze a light source. The screen-to grating distance is 50.0 cm, and

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A spectrometer is used to analyze a light source. The screen-to grating distance is 50.0 cm, and the grating has 5000.0 slits/cm. Spectral lines are observed at the following angles: 12.98°, 19.0°, 26.7°, 40.6°, 42.4°, 63.9°, and 77.6°. 

(a) How many different wavelengths are present in the spectrum of this light source? Find each of the wavelengths. 

(b) If a different grating with 2000.0 slits/cm were used, how many spectral lines would be seen on the screen on one side of the central maximum? Explain.

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