Energy levels in atoms and line spectra
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What does it mean for electron energy levels in isolated atoms to be 'discrete'?
Discrete energy levels mean that electrons within an atom can only occupy specific, quantized energy values. They cannot exist at energy levels between these allowed values.
Describe the formation of an emission line spectrum.
An emission line spectrum is formed when excited electrons in an atom transition to lower energy levels. As they transition, they emit photons with specific energies (and thus wavelengths) corresponding to the energy difference between the levels. These wavelengths appear as bright lines on a dark background.
Describe the formation of an absorption line spectrum.
An absorption line spectrum is formed when atoms absorb photons of specific wavelengths from a continuous spectrum. This occurs when the photon energy matches the energy difference between two electron energy levels within the atom. These absorbed wavelengths appear as dark lines on a continuous, colored background.
State the equation relating photon energy (hf) to the energy difference between two energy levels (E1 and E2). Define all terms.
The equation is hf = E1 – E2, where 'h' is Planck's constant (6.63 x 10⁻³⁴ Js), 'f' is the frequency of the emitted or absorbed photon, E1 is the higher energy level, and E2 is the lower energy level. The difference represents the energy of the photon emitted or absorbed.
An electron transitions from an energy level of -2.0 eV to -5.0 eV. Calculate the frequency of the emitted photon.
First calculate energy difference: |-2.0 - (-5.0)| eV = 3.0 eV. Convert to Joules: 3.0 eV * 1.60 x 10⁻¹⁹ J/eV = 4.8 x 10⁻¹⁹ J. Then use hf = ΔE, so f = ΔE/h = (4.8 x 10⁻¹⁹ J) / (6.63 x 10⁻³⁴ Js) ≈ 7.24 x 10¹⁴ Hz.
Why are emission and absorption spectra considered 'fingerprints' of elements?
Each element has a unique set of electron energy levels, resulting in a unique pattern of emitted or absorbed wavelengths. These patterns are distinct and can be used to identify the element present in a sample (
If an atom absorbs a photon, what must be true about the photon's energy?
The photon's energy must be exactly equal to the energy difference between two of the atom's allowed electron energy levels. If the photon energy doesn't match, it won't be absorbed.
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