1. What is the longest-wavelength EM radiation that can eject a photoelectron from silver, given that the binding energy is 4.73 eV? Is this in the visible range? 2. Find the longest-wavelength photon that can eject an electron from potassium, given that the binding energy is 2.24 eV. Is this visible EM radiation?

1. λ = 2.626 x 10⁻⁷ m = 262.6 nm

This wavelength is not in visible range. It lies in Ultra Violet Region.

2. λ = 5.546 x 10⁻⁷ m = 554.6 nm

This wavelength is in visible range.

Explanation:

The binding energy of in photoelectric effect is also known as work function. The formula for this is given as follows:

Binding Energy = Work Function = hc/λ

λ = hc/Work Function   equation (1)

where,

h = Plank's Constant = 6.626 x 10⁻³⁴ J.s

c = speed of light = 3 x 10⁸ m/s

λ = longest wavelength capable of ejecting electron = ?

(1)

Here,

Work Function = (4.73 eV)(1.6 x 10⁻¹⁹ J/1 eV) = 7.568 x 10⁻¹⁹ J

Therefore,

λ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(7.568 x 10⁻¹⁹ J)

λ = 2.626 x 10⁻⁷ m = 262.6 nm

This wavelength is not in visible range. It lies in Ultra Violet Region.

(2)

Here,

Work Function = (2.24 eV)(1.6 x 10⁻¹⁹ J/1 eV) = 3.584 x 10⁻¹⁹ J

Therefore,

λ = (6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(3.584 x 10⁻¹⁹ J)

λ = 5.546 x 10⁻⁷ m = 554.6 nm

This wavelength is in visible range.

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