In order to comply with the requirement that energy be conserved, Einstein showed in the photoelectric effect that the energy of a photon (hv) absorbed by a metal is the sum of the work function (Φ), the minimum energy needed to dislodge an electron from the metal’s surface, and the kinetic energy (Eκ) of the electron: hv = Φ + Eκ. When light of wavelength 358.1 nm falls on the surface of potassium metal, the speed (u) of the dislodged electron is 6.403105 m/s.
(b) What is Φ (in J) of potassium?

The work function is the smallest amount of thermodynamic effort required in solid-state physics to transport an electron from a solid to a location in the vacuum immediately outside the solid surface.

Calculation of work function Φ:

hv = Φ + KE

where,

KE = 1.866 × 10 ⁻¹⁹ J

threshold frequency, v = c / λ

where,

c = speed of light, 3.0 × 10 ⁸ m/s

λ = wavelength of light = 358.1 nm

= 3.581 × 10⁻⁷ m

v = ( 3.0 × 10 ⁸ m/s ) / (3.581 × 10⁻⁷ m )

= 8.378 × 10¹⁴ s⁻¹

hv = 6.626 × 10⁻³⁴ m² kg/s × 8.378 × 10¹⁴ s⁻¹

= 5.551 × 10⁻¹⁹ J

5.551 × 10⁻¹⁹ J = 1.866 × 10 ⁻¹⁹ J + Φ

Φ = 5.551 × 10⁻¹⁹ J - 1.866 × 10 ⁻¹⁹ J

= 3.685 × 10⁻¹⁹ J

Hence, the Φ of potassium is 3.685 × 10⁻¹⁹ J.

Learn more about work function here:

https://brainly.com/question/24180170

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