Answer:
The wavelength of the incoming photon is 172.8 nm
Explanation:
The wavelength of the incoming photon can be calculated with the photoelectric equation:
[tex] KE = h\frac{c}{\lambda_{p}} - \phi [/tex] (1)
Where:
KE: is the kinetic energy of the electron
h: is Planck's constant = 6.62x10⁻³⁴ J.s
c: is the speed of light = 3.00x10⁸ m/s
[tex]\lambda_{p}[/tex]: is the wavelength of the photon =?
Φ: is the work function of the surface (Iron) = 4.5 eV
The kinetic energy of the electron is given by:
[tex] KE = \frac{p^{2}}{2m} = \frac{(\frac{h}{\lambda_{e}})^{2}}{2m} [/tex] (2)
Where:
p: is the linear momentum = h/λ
m: is the electron's mass = 9.1x10⁻³¹ kg
[tex]\lambda_{e}[/tex]: is the wavelength of the electron = 0.75 nm = 0.75x10⁻⁹ m
Hence, the wavelength of the photon is:
[tex] \frac{(\frac{h}{\lambda_{e}})^{2}}{2m} = h\frac{c}{\lambda_{p}} - \phi [/tex]
[tex]\lambda_{p} = \frac{hc}{\frac{h^{2}}{2m\lambda_{e}^{2}} + \phi} = \frac{6.62 \cdot 10^{-34} J.s*3.00\cdot 10^{8} m/s}{\frac{(6.62 \cdot 10^{-34} J.s)^{2}}{2*9.1 \cdot 10^{-31} kg*(0.75 \cdot 10^{-9} m)^{2}} + 4.5 eV*\frac{1.602 \cdot 10^{-19} J}{1 eV}} = 1.728 \cdot 10^{-7} m = 172.8 nm[/tex]
Therefore, the wavelength of the incoming photon is 172.8 nm.
I hope it helps you!
