<span>Epsilon
zero is permittivity of free space means how much air or vacuum permits
electric field to travel from one charge to other.It is constant in the coulomb
law. This allow Gauss's a lot easier to solve rather than using K</span>
Answer:
The shortest de Broglie wavelength for the electrons that are produced as photoelectrons is 0.81 nm
Explanation:
Given;
wavelength of ultraviolet light, λ = 270 nm
work function of the metal, φ = 2.3 eV = 2.3 x 1.602 x 10⁻¹⁹ J = 3.685 x 10⁻¹⁹ J
The energy of the ultraviolet light is given by;

The energy of the incident light is related to kinetic energy of the electron and work function of the metal by the following equation;
E = φ + K.E
K.E = E - φ
K.E = (7.362 x 10⁻¹⁹ J) - (3.685 x 10⁻¹⁹ J )
K.E = 3.677 x 10⁻¹⁹ J
K.E = ¹/₂mv²
mv² = 2K.E
velocity of the electron is given by;

the shortest de Broglie wavelength for the electrons is given by;

Therefore, the shortest de Broglie wavelength for the electrons that are produced as photoelectrons is 0.81 nm
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for bad things could happen
so think before you act or you'll regret it