The work function of a substance is 4.0eV. Then longest wavelength of light that can cause photoelectron emission from this substance approximately:

The work function of a substance is the minimum energy required to remove an electron from the surface of a substance. This energy is given in electron volts (eV).

The energy of a photon (light particle) is given by the equation E = hf, where h is Planck's constant (6.626 x 10^-34 Js) and f is the frequency of the light.

However, we want to find the wavelength, not the frequency. We can use the equation c = λf, where c is the speed of light (3.00 x 10^8 m/s), λ is the wavelength, and f is the frequency.

We can combine these two equations to get E = hc/λ.

We can rearrange this equation to solve for λ: λ = hc/E.

Substituting the given values:

λ = (6.626 x 10^-34 Js * 3.00 x 10^8 m/s) / 4.0 eV

But we need to convert the energy from eV to Joules because Planck's constant is given in Joules. We know that 1 eV = 1.602 x 10^-19 J.

So, λ = (6.626 x 10^-34 Js * 3.00 x 10^8 m/s) / (4.0 * 1.602 x 10^-19 J)

Solving this gives λ ≈ 7.7 x 10^-7 m, or 770 nm.

So, the longest wavelength of light that can cause photoelectron emission from this substance is approximately 770 nm.