How are units combined/cancelled in this simple equation?

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In summary, the numerical answer is easy to find, but the units for the answer are determined by the energy and frequency of a photon. The unit of frequency is s-1, not s, and the unit of energy is joules. The frequency can be converted to the period, but it appears to be a typing error as it should be measured in inverse seconds. This equation is used to find the energy of a photon based on its frequency.
  • #1
ApoIlo
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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 =
 
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  • #2
The unit of a frequency is s-1, not s.
 
  • #3
Dickfore said:
The unit of a frequency is s-1, not s.

That must be a mistake on my teacher's part, then. Can you explain further? I'm very new to physics.
 
  • #4
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.
 
  • #5
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
 
  • #6
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?
 
  • #7
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.
 
  • #8
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
 

Related to How are units combined/cancelled in this simple equation?

What are units in a scientific equation?

Units in a scientific equation refer to the measurement of a physical quantity, such as length, mass, or time. They are typically represented by symbols, such as meters (m), kilograms (kg), or seconds (s).

How are units combined in an equation?

Units in an equation are combined using mathematical operations such as addition, subtraction, multiplication, and division. The resulting unit of the equation will depend on the units of the individual terms involved in the operation.

What is unit cancellation in an equation?

Unit cancellation, also known as dimensional analysis, is a method of simplifying equations by canceling out units that are present on both sides of the equation. This allows for easier manipulation and understanding of the equation.

How do you know which units to cancel in an equation?

The units that can be canceled in an equation are those that are present on both the numerator and denominator of a fraction or on both sides of an equation. The units that cannot be canceled are those that are unique to one side of the equation.

Why is it important to use units in scientific equations?

Using units in scientific equations is important because it provides context and meaning to the numerical values being used. It also allows for consistency and accuracy in calculations and ensures that the results are in the appropriate unit of measurement.

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