Question

The equation for photon energy, E, iswhere h = 6.626×10^-34 Js (Planck's constant) and c = 2.99×10^8 m/s (the speed of light).What is the wavelength, A, of a photon that has an energy of E= 4.56×10^-19 J?Express your answer numerically in meters.

Answer 1

The energy of a photon is given by:

`\begin{gathered} E=hv \\ E:the\text{ }energy\text{ }of\text{ }a\text{ }particle\text{ }of\text{ }light=4.56*10^(-19)J \\ h:Planck^(\prime)sconstant=6.626*10^(-34)Js \\ v:frequency\text{ }is\text{ }also=(c)/(\lambda) \\ c:speed\text{ }of\text{ }light=2.99*10^8ms^(-1) \\ \lambda:wavelength=?\text{ }(unknown) \end{gathered}`

The formula can be written to solve for the wavelength (lambda):

`\begin{gathered} E=h*(c)/(\lambda) \\ E=(hc)/(\lambda) \\ \lambda=(hc)/(E) \\ \\ \lambda=(6.626*10^(-34)Js*2.99*10^8ms^(-1))/(4.56*10^(-19)J) \\ \lambda=4.34*10^(-7)m \end{gathered}`

Answer: wavelength is 4.34x10^-7 m