Problem 28 - Chemistry The Molecular Science

Question

For which of these transitions in a hydrogen atom is energy absorbed? Emitted? (a) \(n=1\) to \(n=3\) (b) \(n=5\) to \(n=1\) (c) \(n=2\) to \(n=4\) (d) \(n=5\) to \(n=4\)

Step-by-Step Solution

Answer

(a) Absorbed, (b) Emitted, (c) Absorbed, (d) Emitted.

Step 1: Understanding Absorption and Emission

For an electron in a hydrogen atom, energy is absorbed when the electron moves to a higher energy level (from a lower "n" value to a higher "n" value). Conversely, energy is emitted when an electron falls to a lower energy level (from a higher "n" value to a lower "n" value). This is because jumping to a higher orbit requires energy intake, whereas falling to a lower orbit releases energy.

Step 2: Analyzing Transition (a)

Transition from \(n=1\) to \(n=3\): Since the electron is moving from a lower energy level (1) to a higher energy level (3), energy is absorbed.

Step 3: Analyzing Transition (b)

Transition from \(n=5\) to \(n=1\): Here, the electron falls from a higher energy level (5) to a lower energy level (1), so energy is emitted.

Step 4: Analyzing Transition (c)

Transition from \(n=2\) to \(n=4\): The electron moves from a lower level (2) to a higher level (4), indicating that energy is absorbed.

Step 5: Analyzing Transition (d)

Transition from \(n=5\) to \(n=4\): In this case, the electron drops from a higher energy level (5) to a lower level (4), thus energy is emitted.

Key Concepts

Energy Absorption

Energy absorption occurs when an electron transitions to a higher energy level within an atom. This process requires the electron to gain energy. It can be visualized as the electron "jumping" to an outer orbit, which is farther from the nucleus. Here's what's important to know about energy absorption:

• An electron absorbs a precise amount of energy when transitioning to a higher energy level.
• This energy is often provided by electromagnetic radiation, like photons of light.
• When a hydrogen atom absorbs energy, transitions such as from \( n=1 \) to \( n=3 \) or from \( n=2 \) to \( n=4 \) can occur.
• These processes are crucial in understanding phenomena like atomic spectra, where energy absorbed by electrons results in distinct spectral lines.

Whenever you hear about energy absorption, think about an electron moving to a bigger, more distant orbit around the nucleus.

Energy Emission

Energy emission is the opposite of absorption; it occurs when an electron falls to a lower energy level. When this happens, the electron releases the energy it had previously absorbed. This emitted energy often comes out as light:

• The energy released during emission is equal to the energy difference between the two quantum levels.
• In a hydrogen atom, when an electron transitions from \( n=5 \) to \( n=1 \) or from \( n=5 \) to \( n=4 \), energy is emitted.
• The emitted light corresponds to a specific wavelength, contributing to the atom's emission spectrum.

Energy emission is a fascinating process because it accounts for the beautiful array of colors in emission spectra, as electrons return to nearer, more stable orbits.

Quantum Energy Levels

Quantum energy levels, denoted by the principal quantum number \( n \), describe the possible orbits around a nucleus where electrons can exist:

• These levels are quantized, meaning electrons can only inhabit specific energy states. They can't exist between these defined levels.
• The energy associated with each level increases as \( n \) increases, meaning an electron has more energy the farther it is from the nucleus.
• Transitions between these levels explain why atoms absorb or emit energy. Moving from one quantum level to another either requires energy absorption (higher level) or results in energy emission (lower level).

Understanding quantum energy levels is fundamental to grasping atomic and quantum physics, and explains why only certain light frequencies are absorbed or emitted by atoms.