Question

What is the wavelength that has an energy of 3.80×10−19 ? [Hint: Use algebraic manipulation to solve the energy equation for . You will get an answer in meters. Convert it to nanometers .]

Answer 1

\[c= \lambda \nu\]\[E_{photon}=h \nu\]We can solve this second equation for the frequency of the wave...\[\nu = \frac{E_{photon}}{h} \rightarrow \nu = \frac{3.80*10^{-19}J}{6.626*10^{-34}J*s}=5.735*10^{14}s^{-1}\]And then we can plug this back into the first equation...\[\lambda = \frac{c}{\nu} \rightarrow \lambda = \frac{3.00*10^8m*s^{-1}}{5.735*10^{14}s^{-1}}=5.23*10^{-7}m\]\[5.23*10^{-7}m*\frac{1*10^9\ nm}{1\ m}=523nm\]

Answer 2

thanks sooooo much!