Final answer:
Using Einstein's photoelectric equation, the energy of the photon is calculated, from which the kinetic energy and velocity of the emitted electron can be deduced by subtracting the work function and applying conservation of energy principles.
Step-by-step explanation:
To find the maximum kinetic energy (K.E.) and velocity of an electron emitted from metallic potassium when exposed to light of a given wavelength, we will apply Einstein's photoelectric equation and principles of conservation of energy. The photoelectric effect occurs when photons have enough energy to overcome the work function (Φ) of a material and eject electrons.
The energy of a photon (E) is given by the equation E =hv where h is Planck's constant (6.626 x 10-34 J·s) and ν is the frequency of light. The frequency (ν) is related to the wavelength (λ) by the equation ν = c/λ, where c is the speed of light (approximately 3 x 108 m/s).
The maximum kinetic energy of an electron can be found using the equation K. E = E- Φ The work function for metallic potassium is given as 2.0 eV, which we can convert to joules (1 eV = 1.602 x 10-19 J).
Since the question provides the wavelength of the light (350 nm), we first need to find the energy of the photons using wavelength. The velocity of the ejected electron can then be calculated using the equation v =sqrt (2 K.E /m ) where m is the mass of an electron (approximately 9.109 x 10-31 kg).