If you hit the surface of Iron with a photon of energy and find that the ejected electron has a wavelength of .75 nm, what is the wavelength of the incoming photon in nanometers?

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:

Therefore, the wavelength of the incoming photon is 172.8 nm.

I hope it helps you!        

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