If energy is absorbed by a hydrogen atom in its ground...

If energy is absorbed by a hydrogen atom in its ground state, the atom is excited to a higher energy state. For example, the excitation of an electron from the level with $n=1$ to the level with $n=3$ requires radiation with a wavelength of $102.6 \mathrm{nm} .$ Which of the following transitions would require radiation of longer wavelength than this? (a) $n=2$ to $n=4$ (c) $n=1$ to $n=5$ (b) $n=1$ to $n=4$ (d) $n=3$ to $n=5$

If energy is absorbed by a hydrogen atom in its ground state, the atom is excited to a higher energy state. For example, the excitation of an electron from the level with $n=1$ to the level with $n=3$ requires radiation with a wavelength of $102.6 \mathrm{nm} .$ Which of the following transitions would require radiation of longer wavelength than this?
(a) $n=2$ to $n=4$
(c) $n=1$ to $n=5$
(b) $n=1$ to $n=4$
(d) $n=3$ to $n=5$

Key Concepts

Energy Gap and Wavelength Relationship

The wavelength of the photon associated with an electron transition is inversely related to the energy gap between the two levels. A larger energy gap corresponds to a shorter wavelength (and higher energy), while a smaller energy gap corresponds to a longer wavelength (and lower energy). Understanding this inverse relationship is essential for predicting which transitions will absorb or emit radiation of longer wavelengths.

Quantum Energy Levels

Quantum energy levels describe the discrete amounts of energy that electrons can have in an atom. For a hydrogen atom, these levels are quantized and defined by the principal quantum number n. Each level corresponds to a specific energy state, and transitions between these states involve the absorption or emission of energy in the form of photons.

Photon Absorption and Emission

When an atom absorbs or emits a photon, there is a transition between energy levels. The absorption of a photon allows an electron to jump from a lower to a higher energy level, while emission occurs when an electron transitions from a higher to a lower level. The energy of the photon must match the energy difference between these two levels for the process to occur.

Rydberg Formula

The Rydberg formula provides a way to calculate the wavelengths of light involved in electron transitions between energy levels in a hydrogen atom. It relates the inverse of the wavelength to the difference between the reciprocals of the squares of the principal quantum numbers. This formula is crucial in predicting and analyzing spectral lines of hydrogen.

Electron Transition Identification

Identifying electron transitions that involve a smaller energy difference helps determine which transition requires longer wavelength radiation. Analyzing transitions between different quantum states involves comparing the energy differences, where transitions involving higher starting energy levels or smaller differences between final and initial states will often correspond to longer wavelength photons.

Transcript

Please give Ace some feedback