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:
(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
: 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:
(2)
Where:
p: is the linear momentum = h/λ
m: is the electron's mass = 9.1x10⁻³¹ kg
: is the wavelength of the electron = 0.75 nm = 0.75x10⁻⁹ m
Hence, the wavelength of the photon is:
![\frac{(\frac{h}{\lambda_{e}})^{2}}{2m} = h\frac{c}{\lambda_{p}} - \phi](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28%5Cfrac%7Bh%7D%7B%5Clambda_%7Be%7D%7D%29%5E%7B2%7D%7D%7B2m%7D%20%3D%20h%5Cfrac%7Bc%7D%7B%5Clambda_%7Bp%7D%7D%20-%20%5Cphi%20)
Therefore, the wavelength of the incoming photon is 172.8 nm.
I hope it helps you!