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In the formula E = hv, E is measured in Joules and v is measured in Hz, or s^-1. By dimensional analysis, we see that by multiplying kg x m^2 / s by 1/s, we get a units of kg x m^2/s^2. Since Joules is a measure of energy/work, it is equivalent to force x distance. Breaking this down further, force is equivalent to mass x acceleration, which results in units of kg x m/(s^2). Multiplying this by distance gives you kg x m^2/s^2, which is the same as the units for the right side of the E = hv equation.
JedrickZ_3L wrote:Hello can anyone explain to me why Joules in Planck's Constant is kg x m^2 x s? Thanks.
Joules in Planck's Constant is expressed as such because it helps for unit cancellation, depending on what you are solving for one of these two expressions will be easier to visually see how you obtain your final units.
Joules in Planck's Constant can either be expressed by 6.626 x 10^-34 J.S. or 6.636 * 10^-34 kg*m^2*s^-1. Typically, choosing between 6.636 * 10^-34 kg*m^2*s^-1 and 6.626 x 10^-34 J.S. is situational, in which the one that would provide the easiest cancellations would be the best option to use.
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