Does a photon of visible light (λ≈400 to 700 nm) have...

Does a photon of visible light $(\lambda \approx 400$ to $700 \mathrm{~nm})$ have sufficient energy to excite an electron in a hydrogen atom from the $n=1$ to the $n=5$ energy state? from the $n=2$ to the $n=6$ energy state?

Key Concepts

Photon Energy Calculation

This concept involves determining the energy of a photon using the formula E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the photon. Understanding this allows one to assess whether a photon has enough energy to induce a particular electronic transition in an atom.

Quantized Energy Levels

Atoms, such as hydrogen, have discrete energy levels, meaning electrons can only exist in specific energy states. These energy states are characterized by principal quantum numbers and are typically described by models such as the Bohr model in the case of hydrogen. The difference in energy between these levels determines the energy required for an electron to transition from one level to another.

Electronic Transitions

This concept pertains to the movement of an electron between different quantized energy states within an atom. An electron can be excited from a lower energy level to a higher one by absorbing a photon whose energy exactly matches the energy gap between these states. Conversely, an electron will emit a photon of that energy difference when falling back to a lower energy state.

Electromagnetic Spectrum - Visible Light

The visible light region of the electromagnetic spectrum consists of wavelengths approximately between 400 nm and 700 nm. Understanding the energy range corresponding to this region is important when evaluating if photons within this spectral range can initiate electronic transitions in atoms.

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