Photosynthesis » Limiting Factors and Greenhouses
What you'll learn this session
Study time: 30 minutes
AQA spec: 4.4.1.2 (Higher tier only)
- How the factors that affect photosynthesis work together, and why any one of them can be the limiting factor
- How to explain graphs with two or three factors and decide which factor is limiting
- How light intensity changes with distance, using inverse proportion and the inverse square law
- Why limiting factors matter when growing crops in greenhouses and still making a profit
Higher tier only
Everything in this lesson is Higher tier only. Foundation students do not need it.
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Unlock This CourseThe factors work together
In the last lesson you looked at temperature, light intensity, carbon dioxide concentration and chlorophyll one at a time. In a real leaf all of them act at once. They interact, so the rate of photosynthesis depends on all of them together.
Photosynthesis is a bit like a production line. The line can only go as fast as its slowest step. Whichever factor is in the shortest supply is the one that limits the rate. This is the limiting factor you met in the last lesson.
Any one of the factors can be the limiting factor. It can also change. On a bright but cold morning, temperature may limit the rate. Once the sun warms the air, carbon dioxide may become the limiting factor instead. Fixing one problem does not speed things up for ever, because the next factor in short supply takes over.
Key terms:
- Interact: to work together, so that the effect of one factor depends on the others.
Graphs with two or three factors
Some graphs have more than one curve. They show what happens when you change one factor while a second factor is set at different levels. Here is an example. A student measures the rate of photosynthesis at five light intensities, with two different carbon dioxide concentrations. The temperature is kept the same.
Results
Light intensity (units): 1, 2, 3, 4, 5
Rate at 0.04% carbon dioxide (cm3/min): 2, 4, 6, 6, 6
Rate at 0.1% carbon dioxide (cm3/min): 2, 4, 6, 8, 8
Use these steps to decide what is limiting:
- Look at the rising part of a curve. The rate goes up as the factor on the x-axis goes up. So the factor on the x-axis is the limiting factor there. Between 1 and 3 units, light intensity is limiting. Both curves are the same, so the carbon dioxide concentration makes no difference yet.
- Look at the flat part of a curve. Increasing the x-axis factor no longer helps. So something else is limiting. At 4 and 5 units on the 0.04% curve, the rate is stuck at 6. Carbon dioxide is limiting, because the 0.1% curve rises higher.
- Compare the flat parts of different curves. The flat part of the 0.1% curve is at 8, higher than 6. This shows that raising carbon dioxide lifted the plateau.
- Ask what limits the highest flat part. At 0.1% carbon dioxide and 4 or more units of light, the rate is still stuck at 8. Neither light nor carbon dioxide is limiting now. The limiting factor must be a third one, such as temperature or the amount of chlorophyll.
A third factor is usually shown as a third curve on the same graph. For example, a curve for a higher temperature that levels off at a higher rate shows that temperature was the limiting factor on the lower curve.
📈 Line rising
The factor on the x-axis is limiting.
➖ Line flat
The x-axis factor is not limiting. Another factor is.
🔄 New curve higher
The factor that was changed between the curves was limiting.
Worked example
A plant is kept in bright light at 15 °C and gives a flat graph at 5 cm3/min. At 25 °C, with the same light and carbon dioxide, it levels off at 9 cm3/min.
The rate went up when only the temperature was raised, so temperature was the limiting factor at 15 °C.
Light intensity and distance
In a lab, you can change the light intensity by moving a lamp towards or away from a plant. The further away the lamp is, the dimmer the light that reaches the plant. The link between distance and light intensity is not a straight line.
When two quantities are in inverse proportion, one goes down as the other goes up. If you double one, the other halves.
Light intensity is not in simple inverse proportion to distance. It follows the inverse square law: light intensity is inversely proportional to the distance squared. You can write this as:
light intensity ∝ 1 ÷ distance2
This means that if you double the distance, the light intensity falls to one quarter (1 ÷ 22). If you treble the distance, it falls to one ninth (1 ÷ 32).
Worked example
A lamp gives a light intensity of 80 units on a plant 10 cm away. What is the light intensity at 20 cm?
The distance has doubled, so the intensity is divided by 22 = 4.
80 ÷ 4 = 20 units.
Worked example
The same lamp is moved to 30 cm away. The distance is 3 times larger, so the intensity is divided by 32 = 9.
80 ÷ 9 = 8.9 units (to 1 decimal place).
This is why a small move of the lamp when it is close to the plant changes the light intensity a lot, while the same move far away changes it very little.
Key terms:
- Inverse proportion: a relationship where one quantity goes down as the other goes up. Doubling one halves the other.
- Inverse square law: light intensity is inversely proportional to the distance from the light source squared.
Limiting factors in greenhouses
Growers use greenhouses to control the conditions around a crop. Understanding limiting factors tells them what to change to get the maximum rate of photosynthesis, and so more growth.
🔥 Heat
A heater keeps the temperature near the optimum, even on cold days and at night.
💡 Light
Artificial lights give extra light on dull days, so the plants can photosynthesise for more hours.
🍃 Carbon dioxide
Extra carbon dioxide can be added to the air. Burning a fuel such as paraffin gives both heat and carbon dioxide.
Each of these costs money. Heating, lighting and gas all add to the grower's bills. So the aim is not to give plants as much of everything as possible. The aim is to increase the rate of photosynthesis while still making a profit.
The key idea is to find the limiting factor and change only that one. Adding more of a factor that is not limiting wastes money, because the rate does not go up. For example, if the greenhouse is already warm and the light is dim, extra heating costs money and gives no extra growth. Extra light is the right choice.
Growers also look at whether a change is cost effective. The extra crop sold must be worth more than the extra cost of the heat, light or carbon dioxide.
Worked example
A grower pays £200 a month for extra lighting. It increases the crop, adding tomatoes worth £500 a month.
Gain from the change = 500 − 200 = £300 a month. It is worth doing.
Adding a heater costs £300 a month, but the greenhouse is already at the optimum temperature, so temperature is not limiting and the crop does not increase at all.
0 − 300 = −£300. This is a loss, so it is not worth doing.
Common mistakes
Students often say "the plant needs more light" when the graph is flat. A flat line means the factor on the x-axis is no longer limiting, so more of it will not help. Another mistake is to say that the inverse square law means "double the distance, half the light". It is a quarter. Finally, do not say a grower should add as much heat, light and carbon dioxide as possible. Only the limiting factor is worth adding, and only if the extra crop is worth more than the cost.
Exam-style question
A student investigated the rate of photosynthesis in pondweed. She measured the rate at different light intensities with two carbon dioxide concentrations. The temperature was the same for both.
Light intensity (units): 1, 2, 3, 4
Rate at low carbon dioxide (cm3/min): 3, 6, 6, 6
Rate at high carbon dioxide (cm3/min): 3, 6, 9, 12
(a) Give the limiting factor for the low carbon dioxide curve at a light intensity of 3 units. [1 mark]
(b) Explain why the rate on the high carbon dioxide curve is higher at a light intensity of 4 units. [2 marks]
(c) A lamp gives a light intensity of 64 units at 5 cm from the plant. Calculate the light intensity at 10 cm. [2 marks]
Model answer
(a) Carbon dioxide (concentration) (1).
(b) The carbon dioxide concentration is higher, so carbon dioxide is no longer limiting (1). More carbon dioxide means more of the reactant, so the rate can keep rising (1).
(c) The distance is doubled, so divide by 22 = 4 (1). 64 ÷ 4 = 16 units (1).
Exam tip
In part (c), the answer is not 32. When the distance doubles you divide by 4, not 2. Write the "divide by distance squared" step down so you pick up the method mark.