Final answer:
The maximum wavelength of light required to free an electron for a metal with a work function of 3.75 eV is found using the photoelectric effect formula and is approximately 331.7 nm. However, the closest given option is 3145 Å.
Step-by-step explanation:
The question is about finding the maximum wavelength of light that can free an electron from a metal surface with a given work function using the concept of the photoelectric effect. The work function is given as 3.75 eV (electron volts), and we are also given Planck's constant (h) and the speed of light (c).
To find the maximum wavelength, we use the equation E = hν, where E is the energy equivalent to the work function, ν is the frequency, and h is Planck's constant. Since ν = c / λ and E is given in eV, we first convert E to Joules using the conversion factor: 1 eV = 1.602 x 10^-19 J. Then, we can solve for λ, the wavelength:
λ = c / ν = hc / E
By substituting the values, we get:
λ = (6.624 x 10^-34 Js) * (3 x 10^8 m/s) / (3.75 eV * 1.602 x 10^-19 J/eV)
Calculating the above expression, we find that the maximum wavelength (λ) is approximately 331.7 nm, which is not one of the options provided. However, the closest answer from the choices given would be option (a) 3145 Å, noting that 1 Å = 10^-10 m.