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 = Ef – Ei

As a result: Ei – Ef = 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.

Ei = -6.04 eV

Ef = -54.4 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.

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 = ?

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

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

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

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 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

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 1016 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 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 = ?

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

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

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 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

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