Question 6.2: The laser in a standard laser printer emits light with a wav......
The laser in a standard laser printer emits light with a wavelength of 780.0 nm. What is the energy of a photon of this light?
Strategy We know the connection between photon energy and wavelength, which is given by Equation 6.3. Again, care with units requires conversion from nanometers to meters.
E={\frac{h c}{\lambda}} (6.3)
780.0\;\mathrm{nm}\times{\frac{1\;\mathrm{m}}{1\times10^{9}\,\mathrm{nm}}}=7.800\times10^{-7}\,\mathrm{m}
E=~{\frac{6.626\times10^{-34}{\mathrm{\ J\ s}}\times2.998\times10^{8}\,{\mathrm{m\;s}}^{-1}}{7.800\ 10^{-7}\,{\mathrm{m}}}}=2.547\times10^{-19}\ \text J
Analyze Your Answer The result is a very small number. But we should realize that Planck’s constant is incredibly small—many orders of magnitude smaller than the other quantities in the problem. So a very small energy is likely. Beyond that, we can again rely on a general sense of the magnitude of the quantity we are calculating. For visible light, photon energies are typically on the order of 10^{−19} J, which makes our answer seem plausible.
Check Your Understanding An infrared laser for use in a fiber-optic communications network emits at a wavelength of 1.2 μm. What is the energy of one photon of this radiation?