Final answer:
The binding energy of electrons in magnesium, given the longest-wavelength photon that can eject electrons is 337 nm, is approximately 3.68 eV.
Step-by-step explanation:
To find the binding energy of electrons in magnesium for a longest-wavelength photon of 337 nm that can eject electrons, we will use the equation for the photoelectric effect, which relates the energy of a photon to its wavelength:
E = hf = \(\frac{hc}{\lambda}\)
Where:
- E is the energy of the photon,
- h is Planck's constant (6.626 x 10-34 J·s),
- c is the speed of light in a vacuum (3.00 x 108 m/s),
- f is the frequency of the photon,
- \(\lambda\) is the wavelength of the photon.
Converting the given wavelength from nanometers to meters (1 nm = 10-9 m), we can calculate the energy of the photon in joules and then convert it to electronvolts (eV) using the conversion factor 1 eV = 1.602 x 10-19 J:
E = \(\frac{(6.626 x 10-34 J·s) (3.00 x 108 m/s)}{337 x 10-9 m}\) = 5.89 x 10-19 J
E (in eV) = \(\frac{5.89 x 10-19 J}{1.602 x 10-19 J/eV}\) ≈ 3.68 eV
Therefore, the binding energy of electrons in magnesium is approximately 3.68 eV, which corresponds to option a) 3.68 eV.