11.2 – atomic emission spectra b-level with extensions on wave properties of electrons
TRANSCRIPT
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11.2 – ATOMIC EMISSION SPECTRA
B-LEVEL WITH EXTENSIONS ON WAVE PROPERTIES OF ELECTRONS
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OBJECTIVES
WWBAT…
• Calculate the frequency or wavelength of a photon emitted from an atom, or the energy level of an atomic orbital based on atomic emission
• Describe the wave properties of electrons
• Calculate the de Broglie wavelength or momentum of an electron
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REVISITED: ATOMIC EMISSION SPECTRA AND QUANTUM VIEW OF LIGHT
Energy of a photon = hƒ
Energy of an emitted photon from an atom = Ef – Ei
As a result: Ei – Ef = hƒ
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EXAMPLE
Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1.
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EXAMPLE
Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1.
Ei = -6.04 eV
Ef = -54.4 eV
ƒ = ?
λ = ?
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EXAMPLE
Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1.
Ei = -6.04 eV x 1.6 x 10-19 J = -9.66 x 10-19 J
Ef = -54.4 eV x 1.6 x 10-19 J = -8.704 x 10-18 J
ƒ = ?
λ = ?
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EXAMPLE
Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1.
Ei = -6.04 eV x 1.6 x 10-19 J = -9.66 x 10-19 J Ei – Ef = hƒ
Ef = -54.4 eV x 1.6 x 10-19 J = -8.704 x 10-18 J
ƒ = ?
λ = ?c = ƒλ
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EXAMPLEDetermine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1.
Ei = -6.04 eV x 1.6 x 10-19 J = -9.66 x 10-19 J Ei – Ef = hƒ
Ef = -54.4 eV x 1.6 x 10-19 J = -8.704 x 10-18 J -9.66 x 10-19 – (-8.704 x 10-18) = (6.63 x
10-34)ƒ
ƒ = ?ƒ = 7.74 x 10-18 / (6.63 x 10-34) = 1.17 x 1016 Hz
λ = ?c = ƒλ
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EXAMPLEDetermine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1.
Ei = -6.04 eV x 1.6 x 10-19 J = -9.66 x 10-19 J Ei – Ef = hƒ
Ef = -54.4 eV x 1.6 x 10-19 J = -8.704 x 10-18 J -9.66 x 10-19 – (-8.704 x 10-18) = (6.63 x
10-34)ƒ
ƒ = ?ƒ = 7.74 x 10-18 / (6.63 x 10-34) = 1.17 x 1016 Hz
λ = ?c = ƒλ
3.0 x 108 = (1.17 x 1016)λ
λ = (3.0 x 108) / (1.17 x 1016) = 2.56 x 10-8 m
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CHECK YOURSELF
When an electron transitions from n = 4 to n = 2, a photon is emitted with a wavelength of 450 nm. Determine the energy of the n = 4 level.
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CHECK YOURSELFWhen an electron transitions from n = 4 to n = 2, a photon is emitted with a wavelength of 150 nm. Determine the energy of the n = 4 level in eV.
Ei = ? c = ƒλ
Ef = -13.6 eV x 1.6 x 10-19 = 2.18 x 10-18 J 3.0 x 108 = ƒ(1.5 x 10-7)
ƒ = ?ƒ = (3.0 x 108) / (1.5 x 10-7) = 2.0 x 1015 Hz
λ = 900 nm x 10-9 = 4.5 x 10-7 m Ei – Ef = hƒ
Ei – (-2.18 x 10-18) = (6.63 x 10-34)(2.0 x 1015)
Ei = (6.63 x 10-34)(2.0 x 1015) – (2.18 x 10-18)
Ei = -8.5 x 10-19 J / 1.6 x 10-19 = -5.31 eV
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WAVE PROPERTIES OF ELECTRONS
• Electrons, like photons, exhibit wave-particle duality
• When electrons travel, they travel like waves
• Their momentum, mv, is related to their wavelength through the equation mv = h/λ
• This wavelength is called the de Broglie wavelength
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EXAMPLE
A photon emitted when an electron makes the transition from the n = 3 to n = 1 state is incident upon a photoactive metal with a work function of 3.2 eV.
a. Determine the frequency of the emitted photon. (1.17 x 1016 Hz)
b. Find the de Broglie wavelength of an ejected electron with the maximum kinetic energy.
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EXAMPLE
A photon emitted when an electron makes the transition from the n = 3 to n = 1 state is incident upon a photoactive metal with a work function of 3.2 eV.
a. Determine the frequency of the emitted photon. (1.17 x 1016 Hz)
b. Find the de Broglie wavelength of an ejected electron with the maximum kinetic energy.
ƒ = 1.17 x 1016 Hz
φ = 3.2 eV x 1.6 x 10-19 = 5.12 x 10-19 J
KE =?
me = 9.1 x 10-31 kg
v = ?
λ = ?
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EXAMPLE
A photon emitted when an electron makes the transition from the n = 3 to n = 1 state is incident upon a photoactive metal with a work function of 3.2 eV.
a. Determine the frequency of the emitted photon. (1.17 x 1016 Hz)
b. Find the de Broglie wavelength of an ejected electron with the maximum kinetic energy.
ƒ = 1.17 x 1016 Hz KE = hƒ - φ
φ = 3.2 eV x 1.6 x 10-19 = 5.12 x 10-19 J
KE =? KE = ½mv2
me = 9.1 x 10-31 kg
v = ?
λ = ? mv = h/λ
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EXAMPLE
A photon emitted when an electron makes the transition from the n = 3 to n = 1 state is incident upon a photoactive metal with a work function of 3.2 eV.
a. Determine the frequency of the emitted photon. (1.17 x 1016 Hz)
b. Find the de Broglie wavelength of an ejected electron with the maximum kinetic energy.
ƒ = 1.17 x 1016 Hz KE = hƒ - φ
φ = 3.2 eV x 1.6 x 10-19 = 5.12 x 10-19 J KE = (6.63 x 10-34)(1.17 x 1016) – (5.12 x 10-19) = 7.24 x 10-18 J
KE =? KE = ½mv2
me = 9.1 x 10-31 kg 7.24 x 10-18 = ½ (9.1 x 10-31) v2
v = ? = 4.0 x 106 m/s
λ = ? mv = h/λ (9.1 x 10-31)(4.0 x 106) = (6.63 x 10-34)/λ
λ = (6.63 x 10-34)/[(9.1 x 10-31)(4.0 x 106)] = 1.82 x 10-10 m
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CHECK YOURSELF
An excited atom emits a photon, which is then incident on a photoactive metal. An electron with a de Broglie wavelength of 0.85 nm is ejected from the photoactive metal. If the work function of the metal is 4.5 eV, determine the energy of the originally emitted photon.
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CHECK YOURSELFAn excited atom emits a photon, which is then incident on a photoactive metal. An electron with a de Broglie wavelength of 0.85 nm is ejected from the photoactive metal. If the work function of the metal is 2.9 eV, determine the energy of the originally emitted photon.
λ = 0.85 x 10-9 m mv = h/λ
me = 9.1 x 10-31 kg (9.1 x 10-31)v = (6.63 x 10-34)/(0.85 x 10-9)
v = ? v = (6.63 x 10-34)/[(0.85 x 10-9)(9.1 x 10-31)] = 8.56 x 105 m/s
KE = ? KE = ½ (9.1 x 10-31)(8.56 x 105)2 = 3.3 x 10-19 J
φ = 2.9 eV x 1.6 x 10-19 = 4.7 x 10-19 J KE = hƒ – φ 3.3 x 10-19 = (6.63 x 10-34)ƒ – 4.7 x 10-19
ƒ = ? ƒ = (8.0 x 10-19)/(6.63 x 10-34) = 1.2 x 1015 Hz
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OBJECTIVES
WWBAT…
• Calculate the frequency or wavelength of a photon emitted from an atom, or the energy level of an atomic orbital based on atomic emission
• Describe the wave properties of electrons
• Calculate the de Broglie wavelength or momentum of an electron