Upon being struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of 2.97 eV. What is the work function of this metal?

Work Function = 3.53 x 10⁻¹⁹ J = 2.2 eV

Explanation:

The work function of the metal metal can be found as follows:

Energy of Photon = Work Function + K.E

hc/λ = Work Function + K.E

Work Function = hc/λ - K.E

where,

h = Plank's Constant = 6.625 x 10⁻³⁴ J.s

c = speed of light  = 3 x 10⁸ m/s

λ = wavelength of photons = 240 nm = 2.4 x 10⁻⁷ m

K.E = Maximum Kinetic Energy = (2.97 eV)(1.6 x 10⁻¹⁹ J/1 eV) =  4.752 x 10⁻¹⁹ J

Therefore,

Work Function = (6.625 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(2.4 x 10⁻⁷ m) - 4.752 x 10⁻¹⁹ J

Work Function = 8.281 x 10⁻¹⁹ J - 4.752 x 10⁻¹⁹ J

Work Function = 3.53 x 10⁻¹⁹ J = 2.2 eV

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