The work function of a metal is a measure of the energy required to remove an electron from the surface of the metal. The threshold wavelength of the metal, often referred to as the cutoff wavelength or the critical wavelength, is the minimum wavelength of light that can cause photoemission of electrons from the metal surface.
To find the work function (ϕ) of the metal using the threshold wavelength (λ), we can make use of the relationship between the two. The energy of a photon is given by the equation:
E = hc/λ
Where:
- E is the energy of the photon,
- h is Planck's constant (approximately 6.626 x 10^-34 J·s),
- c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s), and
- λ is the wavelength of the photon.
The work function is equal to the energy of the photon at the threshold wavelength. Therefore, we can set E equal to the work function (ϕ) and λ equal to the threshold wavelength to obtain:
ϕ = hc/λ
Now, we can substitute the given threshold wavelength of 2000 angstroms (which is equivalent to 2000 x 10^-10 meters) into the equation:
ϕ = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (2000 x 10^-10 m)
After performing the calculation, the work function (ϕ) of the metal can be determined.