Final answer:
The cutoff wavelength for a metal surface with a photoelectric work function of 4eV is approximately 310 nm, calculated using the equation λ = hc/φ, where h is Planck's constant, c is the speed of light, and φ is the work function converted to joules.
Step-by-step explanation:
The cutoff wavelength for a metal surface with a photoelectric work function of 4eV can be calculated using the relationship between work function (φ), Planck's constant (h), and the speed of light (c). This relationship is given by the equation λ = hc/φ, where λ is the cutoff wavelength, h is Planck's constant (6.626 x 10-34 J • s), c is the speed of light (3.00 x 108 m/s), and φ is the work function in joules.
First, convert the work function to joules by multiplying by the charge of an electron (1eV = 1.602 x 10-19 J), and then insert the values into the equation to find the cutoff wavelength. Note that 1eV = 1.602 x 10-19 J, so 4eV = 4 x 1.602 x 10-19 J = 6.408 x 10-19 J. The equation becomes λ = (6.626 x 10-34 J • s)(3.00 x 108 m/s) / (6.408 x 10-19 J) which simplifies to λ ≈ 310 nm, making this the cutoff wavelength for the metal surface.