When electromagnetic radiation of wavelength 300nm falls on the surface of sodium electrons are emitted with a ke of 1.68 * 10 5 j mol -1 .what is the minimum energy needed to remove an electron from sodium? what is the maximum wavelength that will cause a photoelectron to move

3.83 × 10⁻¹⁹ J;  518 nm  

Step-by-step explanation:

The equation for the photoelectric effect is

hf = Φ + KE  

Data:

λ = 300 nm = 300 × 10⁻⁹ m

KE = 1.68 × 10⁵ J/mol

Calculations:

Part 1. Minimum energy to remove an electron

(a) Calculate the energy of the photon

fλ = c  

 f = c/λ     Divide each side by λ

E = hf

E = hc/λ

E = (6.626× 10⁻³⁴ × 2.998 × 10⁸)/(300 × 10⁻⁹)

E = 6.622 × 10⁻¹⁹ J

(b) Calculate the KE of one electron

KE = 1.68 × 10⁵ × 1/(6.022 × 10²³)

KE = 2.790 × 10⁻¹⁹ J

(c) Calculate the work function

hf = Φ + KE     Subtract KE from each side

Φ = 6.622 × 10⁻¹⁹  - 2.790 × 10⁻¹⁹

Φ = 3.83 × 10⁻¹⁹ J

The minimum energy to remove an electron from a sodium atom

is 3.83 × 10⁻¹⁹ J.

Part 2. Maximum wavelength to remove an electron

The photon must have just enough energy to overcome the work function and leave the electron with zero kinetic energy.

    E = Φ

hc/λ = Φ                      Multiply each side by λ

  hc = Φ λ                   Divide each side by Φ

   λ = hc/ Φ

   λ = (6.626 × 10⁻³⁴ × 2.998 × 10⁸)/(3.83 × 10⁻¹⁹)

   λ = 5.18 × 10⁻⁷ m     Convert to nanometres

   λ = 518 nm

The maximum wavelength that will cause an electron to move is 518 nm.

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