Final answer:
To find the longest wavelength that can be detected by a photoelectric detector with a given work function, use the equation λ = hc/φ, which yields a wavelength of approximately 579 nm for a work function of 3.43 × 10⁻¹¹ J.
Step-by-step explanation:
To calculate the longest wavelength of light that could be detected with a photoelectric detector based on a metal with a work function of 3.43 × 10⁻¹¹ J, we can use the photoelectric equation which relates the work function (φ), the energy of a photon (E), and the wavelength (λ) of the incident light.
The energy of a photon is given by the equation E = hν, where h is Planck's constant (6.626 × 10⁻4 J·s) and ν is the frequency of the radiation. This energy must be equal to or greater than the work function (φ) for electrons to be ejected from the metal surface. The frequency (ν) is related to the wavelength (λ) by the speed of light (c), c = νλ. Therefore, we can combine these equations to solve for the longest wavelength that can eject electrons.
First, rearrange the equation for energy:
E = hν = φ
Substitute the speed of light equation into the energy equation:
E = hc/λ
Now solve for the wavelength (λ):
λ = hc/φ
Substitute the known values:
λ = (6.626 × 10⁻4 J·s) × (3.00 × 10⁸ m/s) / (3.43 × 10⁻¹¹ J)
Calculate the result:
λ = 579.005 nm
Therefore, the longest wavelength of light that can be detected by this photoelectric detector is approximately 579 nm.