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In the equation E(PHOTON) - E(ENERGY REMOVE e-) = E(EXCESS) = Ek(e-), the units for all energies is Joules (J). For E(PHOTON)=hv, the units for h is Joules*second, and the units for v (frequency) is Hertz. For the kinetic energy equation Ek(e-)=0.5mv^2, mass is in kg and v (velocity) is in meters per second. All the units for these variables are SI units, which means that they are standardized.
The unit for energy is joules (J), but another way to think of joules is as kg*(m^2/s^2), which might be easier in this case to cancel out with the other units of the variables in the equation.
The equation can be manipulated to to solve for either "E" for energy or for "wavelength." When solving for energy, you would use joules. When given the energy at any question, you would have to solve for "wavelength" meaning your units would be in M for meters, the answer should always be in nanometers, so you would have to multiply "M" by 1x10^-9.
Joules is the SI unit for energy and in the case of E=hv Energy (Joules) = Planck's constant (Joule*Second) x Frequency (Seconds^-1). The units for Planck's constant is in Joule-second which is the product of joules and seconds. Therefore in the equation, the Seconds will cancel leaving only Joules. Just a heads up, Frequency can be given in the SI unit Hertz (Hz) or the inverse of seconds (s^-1) but these are interchangeable and the value will be the same.
The SI unit for Energy is J(joule) and Joule = kgm^2s^-1. And yes the units are all the same in order for you to subtract from one another. If you are adding/subtracting something, the components must have the same unit!
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