Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? b. from an orbit of radius 2.12 Å to one of radius 8.46 Å

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Identify the initial and final orbits of the electron in the hydrogen atom. The initial orbit has a radius of 2.12 Å, and the final orbit has a radius of 8.46 Å.

Recall that the energy levels of an electron in a hydrogen atom are quantized and can be described by the formula: E_n = -13.6 \frac{1}{n^2} \text{ eV}, where n is the principal quantum number.

Determine the principal quantum numbers (n) corresponding to the given radii. Use the formula for the radius of an orbit in a hydrogen atom: r_n = 0.529 \times n^2 \text{ Å}. Solve for n for both radii.

Compare the initial and final energy levels. If the electron moves to a higher energy level (larger n), energy is absorbed. If it moves to a lower energy level (smaller n), energy is emitted.

Conclude whether energy is emitted or absorbed based on the direction of the transition between the initial and final energy levels.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Levels in Hydrogen

In a hydrogen atom, electrons occupy specific energy levels, which correspond to distinct orbits around the nucleus. The energy of these levels is quantized, meaning electrons can only exist in certain states. The radius of these orbits increases with energy, and transitions between these levels involve the absorption or emission of energy.

Photon Emission and Absorption

When an electron transitions between energy levels, it either absorbs or emits a photon, which is a particle of light. If an electron moves to a higher energy level (further from the nucleus), it absorbs energy, while moving to a lower level results in the emission of energy. The energy of the photon corresponds to the difference in energy between the two levels.

Rydberg Formula

The Rydberg formula provides a way to calculate the wavelengths of the spectral lines of hydrogen. It relates the wavelengths of emitted or absorbed light to the principal quantum numbers of the initial and final energy levels. This formula is essential for determining the energy change associated with electronic transitions in hydrogen.

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Textbook Question

Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?

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Textbook Question

Classify each of the following statements as either true or false: (a) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths (b) a hydrogen atom in the n = 2 state is at a lower energy than one in the n = 1 state (c) the energy of an emitted photon equals the energy difference of the two states involved in the emission.

Textbook Question

Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? a. from n = 4 to n = 2

Textbook Question

Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: a. from n = 3 to n = 6

Textbook Question

a. Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when n = 2 and when n = 6. Calculate the wavelength of the radiation released when an electron moves from n = 6 to n = 2.

Textbook Question

Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. b. Will the light be absorbed or emitted?

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