What is the wavelength of electromagnetic radiation needed to eject 3.0 ev?

4.125 × 10^-7m

Explanation:

The formula for calculating the energy level of electron is expressed as;

∆E = hf

h is the Planck's constant

f is the frequency

f = velocity of light/wavelength

f = c/λ

c is the velocity of light

λ is the wavelength

∆E = hc/λ

Given ∆E = 3.0eV

Since 1eV = 1.6×10^-19Joules

∆E = 3×1.6×10^-19Joules

∆E = 4.8×10^-19Joules

Other given parameters

c = 3×10^8m/s

h = 6.6×10^-34Js

From the formula ∆E = hc/λ

λ = hc/∆E

λ = 6.6×10^-34 × 3×10^8/4.8×10^-19

λ = 19.8×10^{-34+8}/4.8×10^-19

λ = 19.8×10^-26/4.8×10^-19

λ = 19.8/4.8 × 10^{-26-(-19)}

λ = 19.8/4.8 × 10^{-26+19}

λ = 4.125 × 10^-7m

Hence the wavelength of the electromagnetic radiation is 4.125 × 10^-7m

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