Question

Calculate the wavelengths in nanometers and energies in kilojoules per mole (each to 3 sig. figs.) of the first lines in the hydrogen spectrum series where nf = 4, R[infinity] = 1.097 × 10-2 nm⁻¹, and ni is an integer greater than 4. In what region of the electromagnetic spectrum do they fall?

Answer 1

The wavelengths and energies of the first lines in the hydrogen spectrum series where nf = 4 are calculated using the Rydberg formula.

Step-by-step explanation:

To find the wavelengths and energies of the first lines in the hydrogen spectrum series where nf = 4, we can use the formula:

1/λ = R(infinity) * (1/nf² - 1/ni²)

Where λ is the wavelength, R(infinity) is the Rydberg constant, nf is the final energy level, and ni is the initial energy level. Given that R(infinity) = 1.097 × 10-2 nm⁻¹, we can substitute the values and calculate the wavelengths in nanometers. To calculate the energies in kilojoules per mole, we can use the formula:

E = (hc * R(infinity)) / λ

Where E is the energy, h is the Planck constant, c is the speed of light, R(infinity) is the Rydberg constant, and λ is the wavelength. By substituting the values, we can calculate the energy for each wavelength. The first lines of the hydrogen spectrum series where nf = 4 calculated to 3 significant figures are:

These calculated wavelengths fall in the violet to red region of the electromagnetic spectrum.