Given Rydberg constant as `(1.097 x 10^7m^-1)` . Find the longest and shortest wavelength limit of Baler Series.

The study of emission line spectra of a material serve as a fingerprint for identification of the gas. Given Rydberg constant as 1.097 * 10^7m^-1 . Find the longest and shortest wavelength limit of Baler Series.

Longest wavelengths in Balmer series of He^(+1) is

If the wavelength of spectral lines emitted by hydrogen atom is generally expressed as [1/lambda = R(1/m^2) - (1/n^2)] Where R: Rydberg Constant and .n. and .m. are integers. From this, : Write down the expression for Balmer series of spectral lines.

Evaluate int_0^1(x^2+1)dx as the limit of a sum.

Find the sum of the 1^(st) n terms of the series 3+7+13+21+31+ …

Evaluate int_1^3 2 x d x as the limit of a sum.