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(a) Find a symbolic expression for the wavelength $\lambda$ of a photon in terms of its energy $E,$ Planck's constant $h,$ and the speed of light $c,$ (b) What does the equation say about the wavelengths of higher-energy photons?

a. $\frac{h c}{\lambda}$

b. $\begin{array}{l}{\text { According to the equation, the higher-energy photons have a short wavelength }} \\ {\text { because the energy is proportional to } 1 / \lambda .}\end{array}$

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our question for part. They asked us to find a symbolic expression for the wavelength lambda of a photon in terms of its energy planks constant h in the speed of light. See? Okay, well, this can be done by realizing that the energy of a photon is equal to planks Constant h multiplied by the frequency. Okay, but the frequency is equal to the speed of light. See, because that's the speed at which the photon is traveling, divided by the wavelength Lambda. So plugging in that value or excuse me, plugging in that expression for the frequency we find that energy is equal to planks constant h multiplied by the speed of light, divided by the wave. Like so then to find an expression for the wavelength. In terms of energy, place constant and see, we find that wavelength is equal to place constant times the speed of light divided by the energy eat and we can go ahead and box set in as your solution. For part a part B says, what does this equation say about the wavelength of high energy photons? Okay, so really high energy photons are gonna have a smaller wavelength because wavelength and energy are inversely proportional, so we can go ahead and say that we could say wavelength in energy are inversely proportional. Thus, we'll start a new line here we can say that thus, high energy photons have a small wave links. All right, that's our solution for part B.