The work function of a substance is 3.0eV. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately:

To solve this problem, we need to use the equation for the photoelectric effect, which is:

E = hf

where E is the energy of the photon, h is Planck's constant, and f is the frequency of the light.

However, we want to find the wavelength, not the frequency. We know that the speed of light, c, is equal to the frequency times the wavelength (c = λf). We can rearrange this to find that the frequency is equal to the speed of light divided by the wavelength (f = c/λ).

Substituting this into our original equation gives us:

E = hc/λ

We can rearrange this to solve for the wavelength:

λ = hc/E

We know that the work function of the substance, which is the minimum energy needed to remove an electron, is 3.0 eV. We need to convert this to joules, since the other constants are in SI units. 1 eV is approximately 1.6 x 10^-19 joules, so 3.0 eV is 3.0 * 1.6 x 10^-19 = 4.8 x 10^-19 joules.

Planck's constant, h, is approximately 6.63 x 10^-34 joule seconds, and the speed of light, c, is approximately 3.00 x 10^8 meters per second.

Substituting these values into our equation gives us:

λ = (6.63 x 10^-34 J s * 3.00 x 10^8 m/s) / 4.8 x 10^-19 J

Solving this gives us a wavelength of approximately 4.14 x 10^-7 meters, or 414 nanometers. This is the longest wavelength of light that can cause the emission of photoelectrons from this substance.