This question is about an experiment to measure the Planck constant $h$ using light-emitting diodes (LEDs) - OCR - A-Level Physics A - Question 7 - 2013 - Paper 1

In this experiment, the circuit with LEDs of different colors is connected to a power source. Each LED has a corresponding wavelength and is tested by gradually increasing the voltage until the LED lights up. The minimum voltage ($V_{min}$) at which each LED emits light is recorded. This data is then used to plot a graph of $V_{min}$ against $1/\lambda$, allowing for the analysis of the relationship between the energy of the emitted photons and their wavelengths.

To complete the table with average $V_{min}$ values, input the values corresponding to the given wavelengths. Draw the line of best fit on the graph, using the plotted points. The slope or gradient of this line is to be calculated, which should approximate $1.2 \times 10^{-6} \; V m$.

From the equation $e V_{min} = h / \lambda$, if we rearrange, the gradient of the graph ($\frac{V_{min}}{1/\lambda}$) is directly related to the constants $h$, $c$, and $e$. This relationship can be established by recognizing that the gradient can be expressed as $h/e$. Thus, incorporating the speed of light shows that the gradient is equal to $h/c/e$.

To calculate the Planck constant, we will use the gradient found from the line of best fit. If the gradient is determined to be approximately $1.2 \times 10^{-6} \; V m$, we can rearrange the equation mentioned earlier to find $h$. Therefore, applying the previous relationship, we can derive that:

$h = ext{(gradient)} \times c \times e$

Where $c$ is the speed of light and $e$ is the elementary charge. Once substituted with values for $c$ and $e$, you get an estimate for $h$.