Answer:
[tex]5.07\cdot 10^{-7} m[/tex] (507 nm)
Explanation:
First of all let's calculate the energy of the photon absorbed by the electron, This is given by
[tex]E=hf[/tex]
where
h is the Planck constant
[tex]f=8.88\cdot 10^{14} Hz[/tex] is the frequency of the photon
Substituting,
[tex]E=(6.63\cdot 10^{-34}Js)(8.88\cdot 10^{14}Hz)=5.89\cdot 10^{-19} J[/tex]
The energy of the second photon, the one emitted when the electron drops to the intermediate energy level, is 2/3 of this energy:
[tex]E'=\frac{2}{3}E=\frac{2}{3}(5.89\cdot 10^{-19} J)=3.92\cdot 10^{-19} J[/tex]
The relationship between the energy of the photon and its wavelength [tex]\lambda[/tex] is
[tex]E=\frac{hc}{\lambda}[/tex]
where c is the speed of light. Solving for [tex]\lambda[/tex], we find the wavelength:
[tex]\lambda=\frac{hc}{E}=\frac{(6.63\cdot 10^{-34} Js)(3\cdot 10^8 m/s)}{3.92\cdot 10^{-19} J}=5.07\cdot 10^{-7} m[/tex]
The wavelength (λ) of the photon : 5.106.10⁻⁷ m
The photoelectric effect is an electron coming out of a metal because of electromagnetic radiation
One type of electromagnetic radiation is light
Electrons can come out of metal because they absorb electromagnetic energy radiated on metals. There is also kinetic energy released from metal, which is according to the equation:
[tex] \large {\boxed {\bold {E = hf-hfo}}} [/tex]
fo = the threshold frequency of electromagnetic waves
Radiation energy is absorbed by photons
The energy in one photon can be formulated as
[tex] \rm E = h \times f [/tex]
Where
E = energy of light, J
h = Planck's constant (6,626.10⁻³⁴ Js)
f = Frequency of electromagnetic waves, Hz
f = c / λ
c = speed of light
= 3.10⁸
λ = wavelength
The radiation emitted by the nitrogen and absorbed by an electron
E = h. f
E = 6,626.10⁻³⁴. 8.88 × 10¹⁴
E = 5.839.10⁻¹⁹ J
Two-thirds of the energy previously absorbed and emitting a photon
E photon = 2/3 x E electron
E photon = 2/3 x 5.839.10⁻¹⁹ J
E photon = 3.893.10⁻¹⁹ J
[tex]\rm E=\dfrac{hc}{\lambda}\\\\\lambda =\dfrac{hc}{E}\\\\\lambda=\dfrac{6.626\times 10^{-34}\times 3.10^8}{3,893.10^{-19}}\\\\\lambda=5.106.10^{-7}\:m[/tex]
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