Answer to Question #93491 in Quantum Mechanics for jane montgomery

Question

A) If an element has an emission spectrum with bright lines at 400nm and 800nm, where would you expect to see dark lines in the element’s absorption spectrum?

B) Use the Bohr model of the atom to explain why an emission spectrum is a few separate lines, rather than a continuous pattern.

Answer 1

1) The element's absorption spectrum is "antiemission" spectrum, because the same atoms will only absorb the same waves which they would not emit if the atoms are excited. Just look at the picture below. The dark lines' location on a frequency axis for the absorption spectrum correspond to bright lines on the emission spectrum. If we add these spectra, we'll get a continuous spectrum.

2) According to Bohr model of atom, each electron can take only certain energy states (1st postulate). For instance, an electron can't be located at any point around the atom's nucleus or between two certain orbits and still belong to that atom. Also, according to Rydberg formula, we know that the wavelength is proportional to difference of inverse energy states $n$:

$$\lambda=\frac{1}{RZ^2}\Big(\frac{1}{n_1^2}-\frac{1}{n_2^2}\Big)^{-1}.$$

Since $n$ is a natural number, the emission spectrum is discrete.