A harmonic oscillator absorbs a photon of wavelength 6.50 μm when it undergoes a transition from

step 1 Okay, so the energy absorbed by the harmonic oscillator equals the energy of the photon, which i

A harmonic oscillator absorbs a photon of wavelength 6.50 μm...

A harmonic oscillator absorbs a photon of wavelength $6.50 \mu \mathrm{m}$ when it undergoes a transition from the ground state to the first excited state. What is the ground-state energy, in electron volts, of the oscillator?

Key Concepts

Quantum Harmonic Oscillator

A quantum harmonic oscillator is a fundamental model in quantum mechanics that describes systems with a quadratic potential energy. Its energy levels are discrete and given by the formula E? = h?(n + ½), where n is a nonnegative integer and ? is the oscillator’s frequency. This model is widely used to approximate the behavior of molecules, atoms, and other systems near equilibrium.

Zero-Point Energy

The ground state of a quantum harmonic oscillator does not have zero energy; instead, it possesses the zero-point energy, which is the energy remaining when the system is in its lowest possible state. This energy is equal to (1/2)h? and arises from the inherent uncertainty in the system's position and momentum as dictated by quantum mechanics.

Photon Energy

Photon energy is determined by Planck’s relation, E = h?, which links the energy of a photon directly to its frequency. This means that when a photon is absorbed or emitted during a quantum transition, the energy change of the system is exactly equal to the energy of the photon.

Wavelength-Frequency Relationship

The wavelength of light and its frequency are inversely related by the equation ? = c/?, where c is the speed of light and ? is the wavelength. This relationship is crucial for converting the wavelength of an incoming photon into its corresponding energy, thereby connecting electromagnetic radiation parameters with quantum transitions.

Transcript

Please give Ace some feedback