1.The formula for energy in terms of charge and potential difference is E = QV. So 1 eV = (1.6 x 10^-19 coulombs)x(1 volt) = 1.6 x 10^-19 Joules.
2. De Broglie first used Einstein's famous equation relating matter and energy :
\[ E = mc^2 \]
E= energy, m = mass, c = speed of light
2. Using Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation:
\[ E= h \nu\]
E = energy, h = Plank's constant(6.62607 x 10 J s), υ = frequency
3. Since de Broglie believes particles and wave have the same traits, the two energies would be the same:
\[ mc^2 = h\nu
4. Because real particles do not travel at the speed of light, De Broglie subsituted v, velocity, for c, the speed of light.
\[ mv^2 = h\nu \]
5. Through the equation \(\lambda\), de Broglie substituted \( v/\lambda\) for \(\nu\) and arrived at the final expression that relates wavelength and particle with speed.
\[ mv^2 = \dfrac{hv}{\lambda} \]
Hence:
\[ \lambda = \dfrac{hv}{mv^2} = \dfrac{h}{mv}
4 days ago