The following is a diagram of energy states and transitions in the hydrogen atom.

Question

Match each arrow with the correct response below.

A) The emission line with the shortest wavelength.

B) The absorption line with the shortest wavelength.

C) The emission line with the highest energy.

D) The absorption line with the lowest energy.

E) The emission line with the highest frequency.

F) The line corresponding to the ionization energy of hydrogen

Answer 1

These questions can be answered using Planck's equation, E = hf or E = hc/λ where E is the energy of the photon absorbed or emitted, h is Planck's constant, c the speed of light, f is frequency, and λ is wavelength.

The longer arrows represent higher energies and would have higher frequencies and shorter wavelengths and vice-versa for shorter arrows.

Emission lines have down pointing arrows, and absorption lines up pointing arrows. So, for A the answer would be line #4 (longest down arrow, greatest emission photon energy, shortest wavelength.

Try the others yourself.

Answer 2

The Bohr atom model for the square well potential solution of the wave function yields allowed changes in the electron energy due to a transition that are proportional to the reciprocal of the square of the principle quantum number n. In short delta E = -R(1/n2^2 -1/n1^2). For n infinite 1/n^2 is zero and the energy absorbed to ionize the atom-remove an electron from that potential well is R. Here n1 =1. The inner shell quantum number. R is known as the Rydberg constant of proportionality for Hydrogen.

So n at infinity is your ionization line with the greatest energy absorbed and positive value for E.

When n changes to a lower value the 1/n2^2 is greater than 1/n1^2 and the change in E of the electron is negative. The photon adsorbed is positive with energy h nu. This is the Planck relationship for the energy in light. A transition from a higher principle quantum number to a lower number reduces the energy of the electron with emission of light. One could actually plug the values in for n2 and n1 in the Bohr model or in understanding these ideas. longer lines are greater difference and shorter are smaller differences in the energy of the electron. Those going from n larger to n smaller are emissions and vice versa is an adsorption of light. Energy of light is directly proportional to frequency and frequency is inversely proportional to wave-length.

Then assigning the lines in the diagram is quite straight forward..

With all of that background, line 4 represents the emission with the shortest wave length and highest energy.