Sure, let's go through the steps methodically.
### Question 3
a. Define solar cell. (1 mark)
A solar cell is an electrical device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon. Solar cells are constructed from semiconductor materials, such as silicon, which absorb photons and release electrons, resulting in an electric current.
b. Write the equation to calculate the energy associated with a photon. (1 mark)
The energy associated with a photon is given by the equation:
[tex]\[ E = h \nu \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\(6.62607015 \times 10^{-34} \, \text{m}^2 \text{kg} / \text{s}\)[/tex]),
- [tex]\( \nu \)[/tex] is the frequency of the photon.
c. Explain the term 'work function' in the photoelectric effect. (2 marks)
The work function is the minimum amount of energy required to remove an electron from the surface of a solid material to a point in the vacuum immediately outside the solid surface. It is a crucial concept in the photoelectric effect, which occurs when electrons are ejected from the surface of a material after absorbing energy from light (photons) of sufficient frequency. The energy of the incident photon must be greater than or equal to the work function of the material for the photoelectric effect to occur.
d. Calculate the energy of a red-light photon whose wavelength is 700 nm. (2 marks)
First, we need to convert the wavelength from nanometers (nm) to meters (m):
[tex]\[ \lambda = 700 \, \text{nm} = 700 \times 10^{-9} \, \text{m} = 7.00 \times 10^{-7} \, \text{m} \][/tex]
Next, we use the speed of light in a vacuum ([tex]\(c = 3.00 \times 10^8 \, \text{m/s}\)[/tex]) to find the frequency ([tex]\(\nu\)[/tex]):
[tex]\[ \nu = \frac{c}{\lambda} \][/tex]
[tex]\[ \nu = \frac{3.00 \times 10^8 \, \text{m/s}}{7.00 \times 10^{-7} \, \text{m}} \][/tex]
[tex]\[ \nu = 4.285714285714285 \times 10^{14} \, \text{Hz} \][/tex]
Finally, using Planck's equation, we calculate the energy of the photon:
[tex]\[ E = h \nu \][/tex]
[tex]\[ E = (6.62607015 \times 10^{-34} \, \text{m}^2 \text{kg}/\text{s}) \times (4.285714285714285 \times 10^{14} \, \text{Hz}) \][/tex]
[tex]\[ E = 2.8397443499999993 \times 10^{-19} \, \text{J} \][/tex]
So, the energy of a red-light photon whose wavelength is 700 nm is [tex]\(2.8397443499999993 \times 10^{-19}\)[/tex] joules.
