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Answer :
The longest wavelength of light that will release an electron from a magnesium surface is approximately 335 nm.
The energy required to release an electron from a metal surface is given by the work function (Φ). The relationship between energy (E) and wavelength (λ) of light is E = hc/λ, where h is Planck's constant (4.1357 x 10^-15 eV·s) and c is the speed of light (3.00 x 10^8 m/s).
Given the work function of magnesium (Φ) = 3.7 eV, we convert this to joules by multiplying by the conversion factor 1.602 x 10^-19 J/eV to get Φ = 3.7 x 1.602 x 10^-19 J.
To find the longest wavelength, we equate the energy required to the energy of the photon: Φ = hc/λ.
Rearranging for λ: λ = hc/Φ.
Substitute the values: λ = (4.1357 x 10^-15 eV·s * 3.00 x 10^8 m/s) / (3.7 x 1.602 x 10^-19 J).
Calculating gives λ ≈ 335 nm.
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