A hydrogen atom absorbs light of wavelength 486 nm. (a) How much energy did the atom absorb? (b)

step 1 This question is about energy transition in hydrogen atom. So in this case we have hydrogen atom

A hydrogen atom absorbs light of wavelength 486 nm. (a) How...

A hydrogen atom absorbs light of wavelength $486 \mathrm{nm}$. (a) How much energy did the atom absorb?
(b) What are the values of the principal quantum numbers of the initial and final states of this transition?

Key Concepts

Photon Energy Calculation

This concept involves determining the energy of a photon using the relation E = hc/?, where h is Planck's constant, c is the speed of light, and ? is the wavelength of light. This formula connects the wave properties of light to the quantized energy that photons carry, which is essential in understanding how light interacts with matter.

Electron Transitions in the Hydrogen Atom

In a hydrogen atom, electrons reside in quantized energy levels, and transitions between these levels occur when an electron absorbs or emits a photon whose energy matches the difference between these levels. Absorption causes an electron to move from a lower to a higher energy state, a fundamental process in atomic spectroscopy.

Bohr Model of the Hydrogen Atom

The Bohr model describes the hydrogen atom by postulating that electrons move in fixed orbits, each corresponding to a specific energy level given by E_n = -13.6 eV/n². This model provides a theoretical framework to explain why only certain photon energies (or wavelengths) are absorbed or emitted during electron transitions.

Spectral Series (Balmer Series)

The Balmer series is a set of spectral lines in the visible region that arises from electron transitions where the final (or initial, in absorption processes) energy level is n = 2. Recognizing which series a specific wavelength belongs to helps identify the initial and final quantum states involved in the transition.

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