The wavelengths of the visible spectrum range from about 400 nm (purple) to 700 nm (red). Find the angular width of the first-order visible spectrum created by a diffraction grating with 300 lines per millimeter when white light falls on the grating normally.

Determine the maximum frequency and minimum frequency in a) Lyman series. b)Balmer series.

I'm writing a program which generates the emission spectrum of an element with atomic number Z. To do this, I have used the equation:
$\frac{1}{\lambda }=R_{\mathrm{\infty }}{Z}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
Where $n_1$ is the number of the original energy level and $n_2$ is the number of the final energy level and where $n_1>n_2$
However, this does not calculate the intensity of the lines. Is there anyway to model the intensity using $n_1$, $n_2$ and/or $Z$, assuming that the brightest line has an intensity of 1?

What is the smallest-wavelength line in the Balmer series? Is it in the visible part of the spectrum?

Find the approximate temperature of a red star that emits light with a wavelength of maximum emission of 700 nm

Give the reasons of:
1. In a cavity laser, a beam could be transmitted through the cell without being distorted by the cell wall.
2. The statistical weight for most levels are essentially the in dense material.
3. Homogeneous broading.

Lines in one spectral series can overlap lines in another. Use the Rydberg equation to see if the range of wavelengths in the n₁=1 series overlaps the range in the n₁=2 series.

Explain how absorption and emission lines are created in the atom.