\documentclass{article}
\usepackage{graphicx}
\title{Determining the Planck Constant Using LED Light}
\author{}
\date{February 2024}
\begin{document}
	\maketitle
	\section{Abstract}
		To find the value of the Planck constant - which was determined 
		to be $6.xx \times 10^-2x \pm 0.xx$ - the frequency-energy relationship of 
		light was used. In order to determine the energy per photon (E)
		of the light, LEDs were used since in LEDs the E of the light
		emitted is related to the voltage across the diode and the
		elemental charge. The voltages of several LEDs were measured
		and the values for E calculated (E1, E2...).
		To find the frequency the light of the same LEDs was diffracted
		through several gratings, and the angle of diffraction measured 
		with a spectrometer. The angle and the wavelength of the incoming
		light are related by the line-density of the gratings.
		These densities were measured by passing laser-light of a known
		wavelength through the same gratings used for the LEDs as
		(601.2,299.8...), and the wavelength of each LED as (blah...). 
	\section{LED switch-on voltages}
		If one increases slowly from 0 Volts the voltage across an LED,
		it can be observed that the component begins to emit light
		suddenly. This voltage is the switch-on voltage for the given
		LED, and this is the array of voltages which was measured.
		
		To find this voltage, the LED was watched through a black straw
		in a dark room. These two measures blocked out light so that
		the observant eye was sensitive to the change occurring in the
		LED as it switched on. When that happened, the voltage across
		the LED was measured from a multimetre, the supply turned off
		whilst the measurement was recorded, then switched on to
		repeat; for each colour five such readings were taken.
		
		\table{}

		To find the energy content of the light being emitted, the
		measured voltages are multiplied by the fundamental charge
		constant.

		\subsection{Underlying Physics}
		This works because the light is produced in LEDs by the loss
		of electrical potential energy as electrons in the semiconductor
		which composes the LED fall across bands, which corresponds to 
		the voltage across the LED. 
		
		\includegraphic{semiconductor diagram}
		
		Since the work energy required to
		move a charge across a voltage is given by $E=QV$ - and the
		charge being moved is known (i.e. that of an electron), one
		must only know the relevant voltage in order to find the energy
		of the light.
\end{document}