Calculate the wavelength (in nm) of a photon needed to eject an electron with a kinetic energy of 3.93 eV from a metal surface with a work function of Φ = 0.60 eV. {h = 4.136×10-15 ev·s, c = 2.998×1017 nm/s}
To calculate the wavelength of a photon, we can use the relationship between the energy and wavelength of a photon:
E = hc/λ
Where:
E = Energy of the photon
h = Planck's constant (4.136×10-15 eV·s)
c = Speed of light (2.998×1017 nm/s)
λ = Wavelength of the photon
In this case, we need to find the wavelength of a photon that has enough energy to eject an electron from a metal surface with a work function of Φ = 0.60 eV.
The energy of the photon can be calculated by adding the kinetic energy of the electron (3.93 eV) to the work function (0.60 eV):
E = 3.93 eV + 0.60 eV
E = 4.53 eV
Substituting the given values into the equation, we can calculate the wavelength of the photon:
4.53 eV = (4.136×10-15 eV·s)(2.998×1017 nm/s)/λ
To solve for λ, we can rearrange the equation as follows:
λ = (4.136×10-15 eV·s)(2.998×1017 nm/s)/4.53 eV
Now, let's calculate the wavelength:
λ = (4.136×10-15 eV·s)(2.998×1017 nm/s)/4.53 eV
λ ≈ 272 nm
Therefore, the wavelength of the photon needed to eject an electron with a kinetic energy of 3.93 eV from a metal surface with a work function of Φ = 0.60 eV is approximately 272 nm.