Welcome to the World of Quantum Physics!
In this chapter, we are going to explore one of the most mind-bending ideas in science: the photon model. Up until now, you have probably thought of light as a wave (like ripples on a pond). While that is true, it is only half the story!
We are going to learn how light also behaves like a stream of tiny "packets" of energy. Understanding this is the key to unlocking the secrets of the universe at its smallest scale. Don't worry if it feels a bit strange at first—even Einstein found this stuff tricky!
1. What is a Photon?
The photon model suggests that electromagnetic radiation (like light, X-rays, and radio waves) isn't just a continuous wave. Instead, it is made up of "quanta" (singular: quantum).
Think of a photon as a tiny, discrete packet of energy.
The "Water Balloon" Analogy:
Imagine a hosepipe spraying water. From a distance, it looks like a continuous stream (the wave model). But if you look closely, imagine the water is actually made of individual water balloons being thrown one after another. Each balloon is a photon—a single packet that can't be split into smaller pieces.
Key Takeaway: Electromagnetic radiation is quantised, meaning it comes in specific "packets" called photons.
2. Calculating Photon Energy
The energy of a single photon depends entirely on its frequency. The higher the frequency of the radiation, the more energy each photon carries.
We use two main equations to calculate this energy \( E \):
Equation 1: \( E = hf \)
Equation 2: \( E = \frac{hc}{\lambda} \)
What do the letters mean?
- \( E \) is the energy of one photon (measured in Joules, J).
- \( f \) is the frequency of the light (measured in Hertz, Hz).
- \( \lambda \) is the wavelength (measured in metres, m).
- \( c \) is the speed of light in a vacuum (\( 3.00 \times 10^8 \text{ m s}^{-1} \)).
- \( h \) is the Planck constant (\( 6.63 \times 10^{-34} \text{ J s} \)).
Did you know?
A single photon of blue light has more energy than a single photon of red light because blue light has a higher frequency!
Quick Review:
- Higher frequency = More energy.
- Shorter wavelength = More energy (because frequency and wavelength are opposites!).
3. The Electronvolt (eV)
Because photons are so tiny, their energy in Joules is a very small number (usually around \( 10^{-19} \text{ J} \)). Working with such tiny numbers is annoying for physicists, so we use a much smaller unit called the electronvolt (eV).
Definition: One electronvolt is the energy gained by an electron when it moves through a potential difference of 1 Volt.
How to convert:
To convert between Joules and eV, you just need the charge of an electron (\( e = 1.60 \times 10^{-19} \text{ C} \)).
- Joules to eV: Divide by \( 1.60 \times 10^{-19} \)
- eV to Joules: Multiply by \( 1.60 \times 10^{-19} \)
Memory Aid:
Think of the Joule as a "Giant" unit and the eV as an "eXtra-small" unit. To go from the tiny eV to the Giant Joule, you must multiply.
Key Takeaway: The electronvolt is a convenient unit for measuring the very small energies associated with photons and subatomic particles.
4. Estimating the Planck Constant (The LED Experiment)
One of the cool things you can do in the lab is estimate the value of the Planck constant \( h \) using different coloured LEDs (Light Emitting Diodes).
How it works:
An LED only starts to emit light when the potential difference across it reaches a specific threshold voltage (\( V_{0} \)). At this point, the work done on an electron moving through the LED is roughly equal to the energy of the photon it emits.
Step-by-Step Logic:
1. Energy of the electron = \( eV_{0} \)
2. Energy of the photon = \( \frac{hc}{\lambda} \)
3. We assume they are equal: \( eV_{0} = \frac{hc}{\lambda} \)
The Experiment:
- You use several LEDs of different known wavelengths (\( \lambda \)).
- For each LED, you carefully measure the threshold voltage \( V_{0} \) (the exact moment it starts to glow).
- You plot a graph of \( V_{0} \) on the y-axis and \( 1/\lambda \) on the x-axis.
- The gradient of this graph will be \( \frac{hc}{e} \). Since we know \( c \) and \( e \), we can calculate \( h \)!
Common Mistake to Avoid:
When doing the LED experiment, make sure you look at the LED through a black tube. This makes it easier to see exactly when it first starts to glow, which gives you a much more accurate threshold voltage.
Key Takeaway: By equating the electrical energy supplied to an electron to the energy of the emitted photon (\( eV = hf \)), we can experimentally determine the Planck constant.
Chapter Summary
- Photons are discrete packets (quanta) of electromagnetic energy.
- The energy of a photon is calculated using \( E = hf \) or \( E = \frac{hc}{\lambda} \).
- The electronvolt (eV) is a small unit of energy; \( 1 \text{ eV} = 1.60 \times 10^{-19} \text{ J} \).
- LEDs can be used to estimate the Planck constant \( h \) by measuring their threshold voltage and knowing their wavelength.