How are units combined/cancelled in this simple equation?

ApoIlo

The numerical answer is easy to find, but I'm wondering which units are in the answer and how those units are determined. Thanks in advance.

(6.63E-34 J×s)(7.09E14 s) - 2.17E-19 J =

Dickfore

The unit of a frequency is s^-1, not s.

ApoIlo

That must be a mistake on my teacher's part, then. Can you explain further? I'm very new to physics.

Dickfore

The second from the units of Planck's constant cancels with the inverse second from the unit of frequency. The product is left with a unit of energy, namely the energy of the photon with the given frequency.

You can only add and subtract quantities with the same units, namely joules. Here, you subtract the work function of a metal. Your result, the kinetic energy of the photoelectron, is also in joules.

GarageDweller

If I have some kind of periodic phenomenon, the frequency is defined as the inverse of the period, the period is the time it takes for the system to complete one cycle

ApoIlo

I was just given the equation alone and told to simplify it. Is (7.09E14 s) the frequency in this equation? Can I convert it to the period so that the seconds cancel or is it simply a typing error that it was not measured in inverse seconds in the first place?

BruceW

it looks almost certainly like it is a typing error. it should be 7.09E14 s^-1 Which is the frequency of the photon I presume.

GarageDweller

Looks like your teacher was trying to find real equations for your exercise, but made a typo with the units.

P.s. the equation at hand is the relation between a photons energy and its frequency