Photons, the photoelectric effect and line spectra flashcards

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Photon
A quantum (discrete packet) of electromagnetic radiation, with energy E = hf.
Electronvolt (eV)
The energy transferred when an electron moves through a potential difference of 1 V. 1 eV = 1.60 × 10⁻¹⁹ J.
Photoelectric effect
The emission of electrons from a metal surface when electromagnetic radiation of high enough frequency falls on it.
Work function φ
The minimum energy needed to remove an electron from the surface of a metal.
Threshold frequency f₀
The minimum frequency of radiation that will release electrons from the surface of a metal.
Stopping potential Vs
The minimum reverse p.d. across a photocell that reduces the photocurrent to zero; eVs = maximum kinetic energy of the photoelectrons.
Energy level (in an atom)
One of the discrete energies an electron bound in an atom is allowed to have.
Ground state and ionisation energy
Ground state: the lowest energy level. Ionisation energy: the energy needed to remove an electron from the ground state completely (to 0 eV).
Energy of a photon
E = hf (Yes)
Photon energy from wavelength
E = hc/λ (from E = hf and c = fλ). (No — derive it)
Einstein's photoelectric equation
hf = φ + ½mv²max (Yes)
Threshold frequency from work function
f₀ = φ/h (set the maximum kinetic energy to zero). (No — derive it)
Maximum kinetic energy from stopping potential
eVs = ½mv²max (No — learn it)
Photon emitted or absorbed in a transition
hf = E₁ − E₂ (higher level minus lower level): E = hf applied to the gap. (No — learn it)
Converting between eV and J
Energy in J = energy in eV × 1.60 × 10⁻¹⁹. (No — learn it)
Graph of maximum kinetic energy (J) of photoelectrons against frequency
Straight line: gradient = h, intercept on the f axis = f₀, extrapolates to −φ on the energy axis.
Ek(max)–f lines for two different metals
Parallel lines (same gradient h), shifted along the f axis: the metal with the larger work function has the larger f₀.
Gradient of a graph of stopping potential against frequency
h/e (the vertical axis is a p.d., not an energy).
Photocurrent against p.d.: brighter light, same frequency
Same stopping potential, higher saturation current.
Emission line spectrum vs absorption line spectrum
Emission: bright lines on a dark background. Absorption: dark lines on a continuous spectrum, at the same wavelengths.
Arrow on an energy level diagram for emission
Points downwards from the higher level to the lower; its length is the photon energy.
Why does light below f₀ release no electrons, however intense?
One photon gives its energy to one electron. Each photon has hf < φ, and more photons only means more electrons that each fail to escape.
Why is photoelectric emission instantaneous?
Each photon delivers all its energy to one electron in a single interaction; there is no build-up time.
What does the wave model wrongly predict about the photoelectric effect?
Emission at any frequency if the light is bright enough, a delay in dim light, and faster electrons in brighter light.
Why do photoelectrons have a range of kinetic energies?
Electrons below the surface lose energy before escaping; only surface electrons leave with hf − φ.
Why does each element have its own line spectrum?
Each element has its own set of discrete energy levels, so only certain energy gaps — and photon frequencies — are possible.
Why does an atom absorb only certain photons, but can be excited by any fast enough electron?
A photon is absorbed whole, so its energy must exactly match a gap; a colliding electron can give up just part of its kinetic energy.
Wave model vs photon model of light today
Light shows wave behaviour as it travels (diffraction, interference) and particle behaviour when emitted or absorbed (photoelectric effect, line spectra).
Energy of a 450 nm photon in J and eV?
hc/λ = 6.63 × 10⁻³⁴ × 3.00 × 10⁸ ÷ 450 × 10⁻⁹ = 4.42 × 10⁻¹⁹ J = 2.76 eV.
Threshold frequency for a metal with φ = 2.4 eV?
f₀ = 2.4 × 1.60 × 10⁻¹⁹ ÷ 6.63 × 10⁻³⁴ = 5.8 × 10¹⁴ Hz.
300 nm light on a metal with φ = 2.4 eV. Maximum kinetic energy of the photoelectrons?
Photon energy = 4.14 eV; 4.14 − 2.4 = 1.7 eV (2.8 × 10⁻¹⁹ J).
Stopping potential 0.50 V. Maximum speed of the photoelectrons?
½mv² = 0.50 × 1.60 × 10⁻¹⁹ = 8.0 × 10⁻²⁰ J; v = √(2 × 8.0 × 10⁻²⁰ ÷ 9.11 × 10⁻³¹) = 4.2 × 10⁵ m s⁻¹.
An electron drops from −1.6 eV to −4.9 eV. Frequency of the photon?
ΔE = 3.3 eV = 5.28 × 10⁻¹⁹ J; f = ΔE/h = 5.28 × 10⁻¹⁹ ÷ 6.63 × 10⁻³⁴ = 8.0 × 10¹⁴ Hz.
Photons emitted per second by a 2.0 mW, 650 nm laser?
Photon energy = 3.06 × 10⁻¹⁹ J; N = 2.0 × 10⁻³ ÷ 3.06 × 10⁻¹⁹ = 6.5 × 10¹⁵ s⁻¹.
Before using h with an energy given in eV…
Convert to joules (× 1.60 × 10⁻¹⁹). Convert nm to m (× 10⁻⁹) as well.
Intensity or frequency: which changes the maximum kinetic energy?
Frequency only. Intensity changes the number of photons, and so electrons, per second.
Number of photon energies from the 4th level of an atom
n(n − 1)/2 = 6: count every pair of levels.
Photon energy from an energy level diagram
Use the gap between the levels, higher minus lower, never one level's value or the sum.

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