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Energy levels and photon emission questions
Heated gases do not emit a continuous spectrum. They emit a few sharp colours and nothing between, and that pattern of lines is direct evidence that the energy inside an atom comes in fixed rungs.
19 original questions · 57 marks · the energy levels and photon emission notes · Quantum phenomena
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Explain what the sharp lines of an emission line spectrum tell us about the energy of electrons in an atom.
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Each line corresponds to a photon of a definite energy, emitted when an electron falls between two levels (1). Sharp, discrete lines show the electron energies are quantised (only certain values are allowed), not continuous (1).An electron transition releases 3.0 eV of energy. Calculate this in joules (e = 1.60 × 10−19 C).
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3.0 eV = 3.0 × 1.60 × 10−19 (1)
= 4.80 × 10−19 J (1)State the equation relating the frequency of an emitted photon to the energy levels involved.
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hf = E1 − E2 (1), where E1 and E2 are the higher and lower energy levels of the transition (1).State what is meant by the ground state of an atom.
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The lowest energy level of the atom (1).The energy levels of an atom are given negative values. Explain why.
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The zero of energy is taken as an electron just free of the atom, at ionisation (1). A bound electron has less energy than a free one, since energy must be supplied to remove it, so every level lies below zero (1).White light is passed through a cool gas and then through a diffraction grating. Dark lines appear in the otherwise continuous spectrum. Explain why.
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The gas absorbs only photons whose energy exactly matches a gap between two of its energy levels (1). Light of those frequencies is removed from the beam (and re-emitted in all directions), leaving dark lines at those positions (1).An electron falls from a level at −1.5 eV to a level at −3.4 eV. Taking h = 6.63 × 10−34 J s, c = 3.0 × 108 m s−1 and e = 1.60 × 10−19 C, calculate (a) the photon frequency and (b) its wavelength.
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ΔE = (−1.5) − (−3.4) = 1.9 eV (1)
ΔE = 3.04 × 10−19 J (1)
(a) f = ΔE/h = 4.59 × 1014 Hz (1)
(b) λ = c/f = 654 nm (1)A transition releases a photon of energy 2.55 eV. Calculate its wavelength.
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λ = hc/ΔE (1)
= (6.63 × 10−34 × 3.0 × 108)/(2.55 × 1.60 × 10−19) (1)
λ = 488 nm (1)An electron drops from a level at −0.54 eV to a level at −3.40 eV. Calculate the wavelength of the emitted photon.
A photon of wavelength 486 nm is emitted from an atom. Calculate the energy of the transition, in electronvolts.
The red line in the spectrum of atomic hydrogen has a wavelength of 656 nm and is produced by electrons falling to the level at −3.40 eV. Determine the energy of the level from which the electrons fall (h = 6.63 × 10−34 J s, c = 3.0 × 108 m s−1, e = 1.60 × 10−19 C).
A sodium atom has its ground state at −5.14 eV and its first excited level at −3.04 eV. Calculate the frequency of the photon that must be absorbed to raise an electron from the ground state to the first excited level (h = 6.63 × 10−34 J s, e = 1.60 × 10−19 C).
Four of the energy levels of atomic hydrogen are −0.85 eV, −1.51 eV, −3.40 eV and −13.6 eV (the ground state). A line in the ultraviolet spectrum of hydrogen has a wavelength of 122 nm. Deduce which transition produces this line (h = 6.63 × 10−34 J s, c = 3.0 × 108 m s−1, e = 1.60 × 10−19 C).
An atom has levels at 0 eV (ionised), −1.5 eV and −13.6 eV. An electron falls from the −1.5 eV level to the −13.6 eV level. Calculate the wavelength of the photon emitted and state which part of the spectrum it lies in.
An atom has three energy levels: −1.5 eV, −3.4 eV and −13.6 eV. State how many different spectral lines can be produced by transitions between them, and calculate the wavelength of the line with the longest wavelength.
Explain why the line spectrum of each element is unique.
An atom has three energy levels: −0.9 eV, −2.8 eV and −4.6 eV (the ground state). A student claims that all three possible spectral lines lie in the visible range, 400 nm to 700 nm. Deduce whether the claim is correct (h = 6.63 × 10−34 J s, c = 3.0 × 108 m s−1, e = 1.60 × 10−19 C).
An atom has energy levels at −1.0 eV, −2.5 eV and −6.0 eV (the ground state). An electron in the −1.0 eV level returns to the ground state via the −2.5 eV level. State the number of photons emitted and calculate the wavelength of each (h = 6.63 × 10−34 J s, c = 3.0 × 108 m s−1, e = 1.60 × 10−19 C).
A hydrogen atom is in its first excited state, at −3.40 eV. Ionisation corresponds to 0 eV. Determine the maximum wavelength of electromagnetic radiation that can ionise the atom from this state (h = 6.63 × 10−34 J s, c = 3.0 × 108 m s−1, e = 1.60 × 10−19 C).
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