Respuesta :
A photon of light with frequency of 6.165 x 10^14 Hz has a wavelength of 486.6 nm and energy of 4.084x10^-19 J
The energy of a photon is defined as
[tex]E\text{ = h}\times f[/tex]where h is the Planck's constant and f is the frequency.
h is a constant of value h = 6.62607004 × 10^-34 m2 kg / s
and f was given in the question, f = 6.165 x 10^14 Hz (keep in mind that 1 Hz = 1/s)
Then we calculate:
[tex]E=6.165\times10^{14}Hz\text{ }\times6.626\times10^{-34}m2kg/s=4.084\text{ }\times10^{-19}m^2kg/s^2[/tex]Since the unit Joules corresponds to (m^2 kg / s^2), we have that E = 4.084x10^-19 J, and we may calculate the wavelength of the photon considering that:
[tex]\lambda=\frac{c}{f}[/tex]where λ is the wavelength, c is the velocity of light and f is the frequency.
[tex]\lambda=\frac{300000000\frac{m}{s}}{6.165\times10^{14}s^{-1}}=4.866\times10^{-7}m=486.6\text{ }\times10^{-9}m=486.6\text{ nm}[/tex]