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 :

The energy of a photon is given by:

[tex]\begin{gathered} E=hv \\ E:the\text{ }energy\text{ }of\text{ }a\text{ }particle\text{ }of\text{ }light=4.56\times10^{-19}J \\ h:Planck^{\prime}sconstant=6.626\times10^{-34}Js \\ v:frequency\text{ }is\text{ }also=\frac{c}{\lambda} \\ c:speed\text{ }of\text{ }light=2.99\times10^8ms^{-1} \\ \lambda:wavelength=?\text{ }(unknown) \end{gathered}[/tex]

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

[tex]\begin{gathered} E=h\times\frac{c}{\lambda} \\ E=\frac{hc}{\lambda} \\ \lambda=\frac{hc}{E} \\ \\ \lambda=\frac{6.626\times10^{-34}Js\times2.99\times10^8ms^{-1}}{4.56\times10^{-19}J} \\ \lambda=4.34\times10^{-7}m \end{gathered}[/tex]

Answer: wavelength is 4.34x10^-7 m