The longest wavelength of light is 5 × 10⁻⁷ m.
Given,
Wavelength, λ = 395 nm = 395 × 10⁻⁹ m
Kinetic energy, KE = 0.66 eV = 0.66 × 1.6 × 10⁻¹⁹ V
To find,
Longest wavelength, λ₀ =?
We know the photoelectric effect is given as,
hν = (hc/λ₀) + KE
hc/λ = (hc/λ₀) + KE
where,
h = Planck's constant = 6.625 × 10⁻³⁴
c = speed of light = 3 × 10⁸ m/s
Pu all the values in the formula,
hc/λ = (hc/λ₀) + KE
(6.625×10⁻³⁴×3×10⁸)/395×10⁻⁹ = [(6.625×10⁻³⁴×3×10⁸)/λ₀]+ 0.66 × 1.6 × 10⁻¹⁹
(19.875 × 10⁻²⁶)/395×10⁻⁹ = [(19.875 × 10⁻²⁶)/λ₀] + 1.056 × 10⁻¹⁹
0.0503 × 10⁻¹⁷ - 1.056 × 10⁻¹⁹ = (19.875 × 10⁻²⁶)/λ₀
5.03 × 10⁻¹⁹ - 1.056 × 10⁻¹⁹ = (19.875 × 10⁻²⁶)/λ₀
3.974 × 10⁻¹⁹ = (19.875 × 10⁻²⁶)/λ₀
λ₀ = (19.875 × 10⁻²⁶)/(3.974 × 10⁻¹⁹)
λ₀ = 5 × 10⁻⁷ m
Hence, the longest wavelength of light is 5 × 10⁻⁷ m.
I understand the question you are looking for is this:
Light with a wavelength of 395 nm illuminates a metal cathode. The maximum kinetic energy of the emitted electrons is 0.76 eV. What is the longest wavelength of light that will cause electrons to be emitted from this cathode?
Learn more about photoelectric effect calculation here:
https://brainly.com/question/13438182
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