Answer : The frequency of photon is, [tex]4.29\times 10^{14}Hz[/tex] and energy of wave is [tex]2.84\times 10^{-19}J[/tex]
Explanation : Given,
Wavelength of wave = [tex]699nm=699\times 10^{-9}m[/tex]
First we have to calculate the frequency of wave.
Formula used :
[tex]\nu=\frac{c}{\lambda}[/tex]
where,
[tex]\nu[/tex] = frequency of wave
[tex]\lambda[/tex] = wavelength of wave
c = speed of light = [tex]3\times 10^8m/s[/tex]
Now put all the given values in the above formula, we get:
[tex]\nu=\frac{3\times 10^8m/s}{699\times 10^{-9}m}[/tex]
[tex]\nu=4.29\times 10^{14}s^{-1}=4.29\times 10^{14}Hz[/tex] [tex](1Hz=1s^{-1})[/tex]
The frequency of wave is, [tex]4.29\times 10^{14}Hz[/tex]
Now we have to calculate the energy of wave.
Formula used :
[tex]E=h\times \nu[/tex]
where,
[tex]\nu[/tex] = frequency of wave
h = Planck's constant = [tex]6.626\times 10^{-34}Js[/tex]
Now put all the given values in the above formula, we get:
[tex]E=(6.626\times 10^{-34}Js)\times (4.29\times 10^{14}s^{-1})[/tex]
[tex]E=2.84\times 10^{-19}J[/tex]
Thus, the energy of wave is [tex]2.84\times 10^{-19}J[/tex]
