Question

Eventually, all of the excited hydrogen atoms will emit photons until they fall back to the ground state. How many different wavelengths can be observed in this process?.

Answer 1

The number of different wavelengths that can be observed when excited hydrogen atoms emit photons depends on the number of energy levels the electrons can fall to from the excited state. In hydrogen, the energy levels are infinite, so there are an infinite number of possible wavelengths that can be observed.

Step-by-step explanation:

When an excited hydrogen atom falls back to its ground state, it emits photons. The energy levels in hydrogen are quantized, meaning that an electron can only occupy certain energy levels or orbits. Each energy level corresponds to a specific wavelength of light. Therefore, the number of different wavelengths that can be observed when the excited hydrogen atoms emit photons depends on the number of energy levels the electrons can fall to from the excited state.

For hydrogen, the energy levels are given by the Rydberg formula, which is expressed as:

R = 1.097 * 10^7 m^-1
E = -R * (1/n^2)

Where R is the Rydberg constant and n is the principal quantum number. As the principal quantum number increases, the energy levels become closer together, resulting in a larger number of possible energy differences and therefore more observable wavelengths.

So, the number of different wavelengths that can be observed in the process of hydrogen atoms emitting photons depends on the number of energy levels the excited electrons can fall to. This corresponds to the number of possible values for the principal quantum number n. In hydrogen, the energy levels are infinite, so there are an infinite number of possible wavelengths that can be observed.