11.2 – ATOMIC EMISSION SPECTRA B-LEVEL WITH EXTENSIONS ON WAVE PROPERTIES OF ELECTRONS

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

REVISITED: ATOMIC EMISSION SPECTRA AND QUANTUM VIEW OF LIGHT Energy of a photon = hƒ Energy of an emitted photon from an atom = E f – E i As a result: E i – E f = hƒ

EXAMPLE Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1.

EXAMPLE Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1. E i = eV E f = eV ƒ = ? λ = ?

EXAMPLE Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1. E i = eV x 1.6 x J = x J E f = eV x 1.6 x J = x J ƒ = ? λ = ?

EXAMPLE Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1. E i = eV x 1.6 x J = x JE i – E f = hƒ E f = eV x 1.6 x J = x J ƒ = ? λ = ?c = ƒλ

EXAMPLE Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1. E i = eV x 1.6 x J = x JE i – E f = hƒ E f = eV x 1.6 x J = x J-9.66 x – ( x ) = (6.63 x )ƒ ƒ = ?ƒ = 7.74 x / (6.63 x ) = 1.17 x Hz λ = ?c = ƒλ

EXAMPLE Determine the wavelength of a photon emitted by the above atom when an electron makes a transition from n = 3 to n = 1. E i = eV x 1.6 x J = x JE i – E f = hƒ E f = eV x 1.6 x J = x J-9.66 x – ( x ) = (6.63 x )ƒ ƒ = ?ƒ = 7.74 x / (6.63 x ) = 1.17 x Hz λ = ?c = ƒλ 3.0 x 10 8 = (1.17 x )λ λ = (3.0 x 10 8 ) / (1.17 x ) = 2.56 x m

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.

CHECK YOURSELF When 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. E i = ?c = ƒλ E f = eV x 1.6 x = 2.18 x J3.0 x 10 8 = ƒ(1.5 x ) ƒ = ?ƒ = (3.0 x 10 8 ) / (1.5 x ) = 2.0 x Hz λ = 900 nm x = 4.5 x mE i – E f = hƒ E i – (-2.18 x ) = (6.63 x )(2.0 x ) E i = (6.63 x )(2.0 x ) – (2.18 x ) E i = -8.5 x J / 1.6 x = eV

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

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 Hz) b.Find the de Broglie wavelength of an ejected electron with the maximum kinetic energy.

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 Hz) b.Find the de Broglie wavelength of an ejected electron with the maximum kinetic energy. ƒ = 1.17 x Hz φ = 3.2 eV x 1.6 x = 5.12 x J KE =? m e = 9.1 x kg v = ? λ = ?

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 Hz) b.Find the de Broglie wavelength of an ejected electron with the maximum kinetic energy. ƒ = 1.17 x HzKE = hƒ - φ φ = 3.2 eV x 1.6 x = 5.12 x J KE =?KE = ½mv 2 m e = 9.1 x kg v = ? λ = ?mv = h/λ

EXAMPLE

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.

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 2.9 eV, determine the energy of the originally emitted photon. λ = 0.85 x mmv = h/λ m e = 9.1 x kg(9.1 x )v = (6.63 x )/(0.85 x ) v = ?v = (6.63 x )/[(0.85 x )(9.1 x )] = 8.56 x 10 5 m/s KE = ?KE = ½ (9.1 x )(8.56 x 10 5 ) 2 = 3.3 x J φ = 2.9 eV x 1.6 x = 4.7 x JKE = hƒ – φ  3.3 x = (6.63 x )ƒ – 4.7 x ƒ = ?ƒ = (8.0 x )/(6.63 x ) = 1.2 x Hz

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