AH 3.1.1 Black Body Radiation & 3.1.2 The Photoelectric Effect Flashcards
Describe and explain what is meant by a black body.
A black body is an ideal body or surface that completely absorbs all radiant energy falling upon it with no reflection and that radiates at all frequencies with a spectral energy distribution dependent on its absolute temperature.
Look at the graph below.
a) What to these curves represent?
b) In words, describe the releationship between the radiation peaks and the temperature of the black body.
c) In terms of energy, what is the difference between a high peak and a low peak in the graph?
The colour of the curve in the diagram inicates the colour of EM radiation emitted at peak wavelength.
d) Only one blackbody shown peaks outside the visible wavelength band - what is it’s temperature and peak wavelength approximately?
a) The radiation curves for several different black bodies, each at a different temperature.
b) The hotter the black body, the higher the radiation peak.
c) A high peak means a higher energy density emitted i.e. more Joules emitted per cubic metre at a given wavelength.
d) 3500 K. This blackbody peaks at a wavelength of around 840 nm, from the graph.
The graph below shows several black body radiation curves as well as another line indicated with the red arrow.
a) Explain what this line represents.
b) What maximum value of emitted energy density does this line suggest occurs?
c) Is this possible in reality?
d) What name was given to the problem presented to physicists by this line before black body radition curves were fully understood?
a) This line shows what classical (19th century pre-quantum theory) physics predicted would be the radiation curve for a black body as understood at the time.
b) The classical curve suggested that as the wavelength of the emitted radiation decreased (frequency increased) then the irradiance would tend to infinity!
c) No! Infinite quantities are meaningful in mathematics but not in physical reality.
d) The ultra-violet catastrophe
Explian what is meant by the ultraviolet catastrophe.
The ultraviolet catastrophe was a prediction of early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation of infinite irradiance.
The graph below shows the radiation curves for several different black bodies.
a) Which curve emits most energy overall?
b) Explain how you deduced this from the graph.
a) The black body at 5500 K
b) The area under the 5500 K curve is greatest.
As the y-axis measures irradiance (energy density), the greater the area under the curve, the greater the total energy emitted.
The graph below shows several black body radiation curves for bodies at different temperatures.
As you can see, each black body, irrespective of its temperature, emits radiation over a wide range of wavelengths.
However, each body does not emit radiation with the same irradiance (W m-2) at all wavelengths - some wavelengths are emitted with greater irradiance than others.
There is a Law in the form of an equation which relates the black body’s temperature T and it’s peak emission wavelength λmax
a) State this equation, name each symbol and state it’s unit.
b) What is the Law called?
a) λmax = b/T
λmax = peak radiation wavelength (m)
b = Wein’s Displacement constant (m K)
T = temperature (K)
b) The above equation is Wein’s Displacement Law.
In the constellation of Orion, the Hunter, the star Betelgeuse has a temperature T = 3300 K.
Find the peak wavelength emitted by Betelgeuse and so suggest its colour.
λmax = b/T = 2.898 ×10−3 / 3300
= 8.782 x 10-7 m
λmax = 878 nm
This peak is somewhere in the infra-red, ( λ > 700 nm) as a glance at the graph below will confirm.
So Betelgeuse will appear reddish-yellow.
This is shown in the radiation curve for a black body at 3300K below.
Describe and explain Planck’s quantisation theory.
Plack suggested that energy is quantised, that is exists in multiples of discrete ‘packets’ or quanta.
Explain how Planck’s quantisation theory explains black body radiation curves and so the solves the problem of the ultraviolet catastrophe.
Planck realises that the Law of Conservation of Energy prevented an infinite irradiance.
His quantisation of enrgy using the Planck Equation E-hf, led to his developing equations for the black body curves that ensured they decreased again at wavelengths
Describe and explain the photoelectric effect.
The phoelectric effect is a physicsal phenomenon in which a sufficiently energetic single photon of EM radiation releases a single electron form a metal surface as explained in the image below.
The effect cannot be explained using a wave theory of light as this model cannot accomodate the necessary one-to-one corespondence between photon and electron.
Explain why classical physics could not explain the photoelectric effect.
The photoelctric effect cannot be explained using a classical (wave) theory of light as this model cannot accomodate the necessary one-to-one corespondence between photon and electron.
The clasical theory would say that light which is not energetic enough to casue photoemission in a certain metal could be made to do so by simply increasing the irradiance of the light source (more W m-2 of light). However, this does not happen.
Only the photoelectric thoery of photons can explain the phenomenon.
Describe and explain Einstein’s quantisation theory
It was Einstein who used Planck’s ideas of the quantisation of energy to explain the photoelectric effect.
Eistein developed the photelecric equation E=hf
E = energy of a single photon of light (J)
h = Planck’s constant (J s)
f = frequency of light wave (Hz)
Use Einstein’s quantisation theory to explain the photoelectric effect.
The work function of Sodium is 3.8x10-19 J.
a) Calculate the minimum frequency of electromagnetic radiation that will cause photoemission from Sodium.
b) Find the wavelength of this radiation .
c) Is this radiation visible? If so, state its colour. If not, what type of radiation is it?
