This is because Einstein's theory claims that the energy of each photon is directly proportional to the frequency of the light wave.
E = h.f Energy = Planck's constant × frequency
We can use the wave equation in conjunction with Einstein's equation to see which colour of light offers more energy.
c = f.λ Speed = wavelength × frequency
The red part of the spectrum has the largest wavelength with around 700 × 109 m compared with violet, which has a wavelength of about 400 × 109 m.
The speed of light as with all electromagnetic waves is 3 × 108 m/s.
We also know that Planck's constant has the value of 6.63 × 10-34 Js
E = constant × c
λ
The equation above therefore shows that the larger the wavelength the lower the energy.
Hence the red light is likely to produce less energy than a blue light.
E = 6.63 × 10 -34 × 3 × 10 8
5.5 × 10 -7
Analysing how colours affect solar cell output, would give qualitative results as the variable is discontinuous, but will require expensive and complex technology such as lasers to accurately conduct the experiment.
Distance-
Distance directly affects the light intensity of a source.
Intensity, measured in Watts/m2 is calculated by dividing Power by the area.
I = P _ Intensity = Power/Area
4πr2
Light spreads in an expanding sphere causing an expanding area of where light reaches where the distance increases.
Therefore as distance increases intensity goes down and therefore the solar cell power output cell is reduced.
This variable will be easy to control and give us quantitative results.
Therefore we will test the effect this variable has on solar cell output.
Power-
Power means the amount of energy transfer per unit of time (seconds), V.I
Increasing the amount of the power produced by the light bulb would increase the energy per second being emitted from the source and hence causing a larger output from the solar cell.
This variable is again very easy to control using a simple device such as a rheostat and again this will give us quantitative results.
Therefore we can test this factor and its affect on solar cell output.
Hypothesis:
Distance-
As discussed earlier we know that distance directly affects light intensity.
This is because light spreads from the source in an expanding sphere.
As intensity equals Power/Area we need to calculate the area of the sphere.
The area of the sphere is equal to:
Area of Sphere = 4.π.r2 where r = distance from the light source.
If r is doubled then the Area of the sphere is quadrupled as shown below.
A = 4.π.r2
Now double the distance from the light source to get:
A = 4. π. (2r) 2
A = 4. π.4r2
A = 4 × 4.π.r2
This shows that there will be a y α x2 correlation if y = area and x = distance from source.
This concept can also be shown in a diagram.
[Diagram]
Other experiments also show this correlation.
[Diagrams]
Now that we have established that there is a A α d2 relationship we can see from the intensity formula
I= Power/area that as area has a squared relationship with distance then Intensity will have a 1/x2 relationship with distance where distance = x, if the power stays constant.
As intensity has a 1/x2 relationship with distance so will the solar cell output.
This is known as Inverse Square Law.
This law is also observed with correlations of other electromagnetic waves such as gamma radiation, with distance, that is why tweezers should be used to handle radioactive sources.
The inverse square law would mean that we should get a graph (predicted) as shown below.
[Graph of y = 1/x2]
What this means in scientific terms is that photons ('small packets' of light energy) usually hit a solar cell and sometimes dislodge electrons from the semiconductor, into motion inducing a small current.
As the distance increases between the solar cell and the light bulb the same number of photons are spread out over an area of an imaginary sphere, which expands in proportion to the square of the distance.
It therefore means, as distance varies the inverse of the distance squared proportion of photons hit a unit of area per second and that's why the amount of current produced should also have the same relationship.
Power-
Power is a much simpler factor when it comes to light intensity.
As the Intensity = Power/area(constant).
This means that the increase light intensity is proportional to the increase in power, given that the distance is constant.
This will provide a y = m.x + c line on a graph as shown below.
[Graph]
In scientific terms this means that there will be more photons generated by the light bulb per second therefore meaning that there will be more photons hitting a specific unit area per second.
The correlation should be proportional.
Skill Area O: Obtaining evidence
Activities chosen should enable pupils to develop their abilities in the aspects listed below.
- Use the equipment to perform the practical in an appropriate way to meet the demands of the activity.
- Pay proper regard to safety precautions in the way in which the equipment is used.
- Make an appropriate number of observations or measurements to meet the requirements of the activity.
- Record the observations or measurements in a clear way.
- Recognise the need for precision and accuracy when observing or measuring.
- Repeat observations or measurements when necessary.
- Recognise the need for reliable evidence.
Candidates should be taught:
a to use a range of apparatus and equipment safely and with skill;
b to make observations and measurements to a degree of precision appropriate to the context;
c to make sufficient relevant observations and measurements for reliable evidence;
d to consider uncertainties in measurements and observations;
e to repeat measurements and observations when appropriate;
f to record evidence clearly and appropriately as they carry out the work.
MARK DESCRIPTIONS: The mark descriptions are designed to be hierarchical.
6 marks
O.6a make sufficient systematic and accurate observations or measurements and repeat them when appropriate
- Use your equipment to obtain the results as accurately as possible.
- Make sure your results are spread out over a good range.
- Make sure that you have enough results to allow you to draw a conclusion.
- If you think that some of your results could vary a lot then take some repeat readings
O.6b record clearly and accurately the observations or measurements
- Use a clear way of accurately recording your results.
- Perhaps use a table of results with clear headings and correct units for measurements.
8 marks
O.8a use equipment with precision and skill to obtain and record reliable evidence which involves an appropriate number and range of observations or measurements
- Use equipment that will help you to obtain precise results.
- Make sure that the number and range of results that you have are sufficient to allow you to draw a firm conclusion.
- If possible repeat results in order to obtain average readings that are then more reliable.
- Record the results in a clear and accurate way.
Apparatus:
12V power supply
25W tungsten filament bulb with lamp
Low efficiency Solar cell
Ruler
Analogue Ammeter
Analogue Voltmeter
Analogue Milliammeter
Method:
The apparatus will be connected up as shown below.
[Circuit diagrams]
As I predict light intensity will decrease rapidly as the distance between the bulb and cell increases, we must have a rather small range.
When testing the effect of distance I connect up the circuit and establish what the constant power output is, then I will take readings from the Milliammeter every time I move the solar cell 1cm from 0-15 cm.
This will give us plenty of readings so I can easily establish a pattern in the experiment.
When testing the effect of the power input I plan to hold the cell 1cm away from the bulb (this will give relative high readings), then move the knob on the rheostat a few centimetres (to increase resistance) and then take readings from the voltmeter and the ammeter (multiplying the two would give power input in Watts).
Both experiments will be repeated to increase the accuracy but not averaged as there are too many variables.
Fair Test-
In order to make it a fair test we try to keep the two other factors constant while the other is being tested.
This included maintaining white light being generated by the light bulb throughout, maintaining constant power output using accurate readings of volt/ammeters (when varying distance) and keeping the distance between the bulb and the solar cell at 1 cm (when varying power).
Background radiation and reflections of the white light could cause anomalies in the data so it is important to keep the conditions constant, i.e. the same number of lights on in the lab.
Over-heating of the bulb (causing increase in resistance) and the solar cell (resulting in fall of resistance) are also sources of error but are mainly unavoidable with the time constraints, but the power will not be turned on until its necessary to obtain a reading.
Safety
The experiment is very safe, the only thing to remember is that:
DO NOT TOUCH THE LIGHT BULB
DO NOT CONNECT THE MILLIAMMETER TO THE LIGHT BULB CIRCUIT
Results:
Table 2. 1: Table of results for Power input in the light bulb against Solar cell output
Table 2. 2: Distance against solar cell output.
Table 2. 3:
Table 2. 4 Distance against solar cell output (2).
SKILL AREA A: ANALYSING EVIDENCE AND DRAWING CONCLUSIONS
Activities chosen should enable pupils to develop their abilities in the aspects listed below.
- Choose the most appropriate way of presenting the results to show the experimental findings.
- Construct diagrams, charts or graphs where appropriate to display results.
- Use numerical methods to process results, where appropriate.
- Make use of diagrams, charts, graphs or numerical methods in order to reach conclusions.
- Identify patterns or trends in the results.
- Draw meaningful conclusions that are consistent with the results obtained.
- Make use of scientific knowledge and understanding to explain conclusions.
Candidates should be taught:
a to present qualitative and quantitative data clearly;
b to present data as graphs, using lines of best fit where appropriate;
c to identify trends or patterns in results;
d to use graphs to identify relationships between variables;
e to present numerical results to an appropriate degree of accuracy;
f to check that conclusions drawn are consistent with the evidence;
g to explain how results support or undermine the original prediction when one has been made;
h to try to explain conclusions in the light of their knowledge and understanding of science.
MARK DESCRIPTIONS: The mark descriptions are designed to be hierarchical.
6 marks
A.6a construct and use appropriate diagrams, charts, graphs (with lines of best fit), or use numerical methods, to process evidence for a conclusion.
- Use the best way of displaying your results clearly by using a chart, diagram, line graph or by doing calculations that help you to make good use of your results.
A.6b draws a conclusion consistent with their evidence and relates this to scientific knowledge and understanding
- Make use of your results and any processing that you have done to write a sensible conclusion that explains what has been found out.
- Say what scientific knowledge helps to explain your conclusion.
8 marks
A.8a use detailed scientific knowledge and understanding to explain a conclusion drawn from processed evidence
- Use the best way of processing your results e.g. diagrams, graphs, calculations.
- Use this work to draw a meaningful conclusion for the experiment.
- Use scientific knowledge in a detailed way to explain the conclusion that you have written.
A.8b explains how results support or undermine the original prediction when one has been made.
- If you made a prediction of what you thought would happen, say if your results turned out the way you expected.
- If they did turn out as expected, explain how well the two match.
- If they did not turn out as expected, explain why you think these differences happened.
Analysis
From the data recorded and calculated in the tables above from the tables above we can represent it visually by plotting graphs.
The first graph shows Output current against distance.
There is a distinct y=1/x or y=1/x2 correlation as the graphs fall at a sharp gradient and then at about the 3cm mark the gradient shallows as the graphs curves off.
This does not show a direct relationship between solar cell output and distance, as a straight cannot be established here.
However, it is possible to try Output current against 1/distance or Output current against 1/distance2 as this may produce a straighter correlation.
The next graph is Output current against 1/distance: this shows a slight curve where the line rises at a lower gradient at the beginning and then rises at faster rate, i.e. resembling a y=x2 curve.
The next graph plots the results of Output current versus 1/distance 2 on: This time the best line of fit is a straight line.
This therefore shows that the square root of the inverse of the solar cell output is proportional to the distance between the bulb and the cell.
In other words the solar cell output is proportional to the inverse square of the distance i.e. Output is proportional to 1/d2.
Hence this is an example of inverse square law.
The last two graphs show the relationship between solar cell output and the power emitted from the bulb (one for each experiment).
Again both are very similar.
The two graphs show a nearly straight correlation but a very slight curve a little like a y=x2 curve.
The curve of the graphs are more likely to have equation of around y = x1·5.
Conclusion:
From plotting the graphs and analysing them we can conclude various points.
After analysing the graphs of solar cell output and √1/cell output against distance, we can establish that there is evidence of inverse square law.
That is to say that the √1/cell output gives a straight line when plotted against distance, which is the same as plotting solar cell output against 1/distance2.
In other words there is evidence to suggest that solar cell output is proportional to the inverse square of the distance between the cell and the bulb.
This trend was predicted in the hypothesis: Solar cell output will have a 1/x2 relationship with distance. Therefore we can evidently see that the hypothesis regarding the relationship between solar cell output and distance has been fully supported.
The reason for this relationship is that light spreads out in an ever-expanding spherical shape.
The surface area of the sphere increases in proportion to the square of the increase of distance between the cell and the bulb.
But as area is the variable denominator in the intensity formula, it means that if area doubles intensity would halve.
However, according to our first point there is a square relationship with area and distance, meaning if distance is doubled, area will be quadrupled and intensity would be quartered.
Hence giving us inverse square law.
This can be explained scientifically.
The same number of photons of light are being emitted per second (as power is constant) by the bulb.
But as the distance between the cell and bulb is increasing, the area of where the photons are hitting is increasing by the square of the distance, hence only the inverse squared number of photons are hitting the cell every second as the distance increases.
