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A student carries out an experiment to determine the value of Planck's constant hₗ, using various LEDs - Scottish Highers Physics - Question 14 - 2023
Question 14
A student carries out an experiment to determine the value of Planck's constant hₗ, using various LEDs. An LED that produces light of known frequency f is connected... show full transcript
Worked Solution & Example Answer:A student carries out an experiment to determine the value of Planck's constant hₗ, using various LEDs - Scottish Highers Physics - Question 14 - 2023
Step 1
Using the square-ruled paper on page 40, draw a graph of 1/V against f.
Answer
To draw the graph,
- Label the x-axis as frequency (f) in ×10¹⁴ Hz and the y-axis as 1/V (1/Volts).
- Plot the data points from the table provided. For example:
- For f = 1.0 × 10¹⁴ Hz, V = 1.38 V, calculate 1/V = 0.726.
- Continue this for all data points.
- Draw a best-fit line through the plotted points.
Step 2
Calculate the gradient of your graph.
Answer
To find the gradient:
-
Choose two points on the best-fit line. Let's assume the points are (5.0, 2.50) and (6.0, 2.64).
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Use the formula for the gradient:
ext{Gradient} = rac{(y_2 - y_1)}{(x_2 - x_1)}
Substituting the values yields: ext{Gradient} = rac{(2.64 - 2.50)}{(6.0 - 5.0)} = rac{0.14}{1.0} = 0.14.
Step 3
Using the gradient of your graph, determine a value for Planck’s constant h.
Answer
To calculate Planck's constant:
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Recall the formula relating frequency, switch voltage, and Planck's constant: e = hf.
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Given e is the charge of an electron, approximately e = 1.60 × 10⁻¹⁹ C.
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Substitute the gradient value into the formula:
h = rac{e}{ ext{Gradient}} = rac{1.60 imes 10^{-19} C}{0.14}.
This results in:
Step 4
Suggest one improvement to the experiment the student could make that would improve the accuracy of their final result.
Answer
One possible improvement could be to repeat the measurements several times for each LED and take the average of the V readings to minimize errors. Alternatively, the experiment could be conducted in a dark room to reduce ambient light interference when the LED emits light.