Answer:
λ ≈ 4.18 x 10^(-7) meters
Step-by-step explanation:
The energy required to remove an electron from an atom is related to the energy of the photon that can do this through the use of the photoelectric effect equation:
E = h * f
Where:
E is the energy of the photon
h is Planck's constant (approximately 6.626 x 10^(-34) J·s)
f is the frequency of the light
To find the maximum wavelength (λ) of light capable of removing an electron, we can use the speed of light (c) equation:
c = λ * f
Where:
c is the speed of light (approximately 3.00 x 10^8 m/s)
λ is the wavelength of light
f is the frequency of light
We can rearrange this equation to find the frequency:
f = c / λ
Now, we can substitute this expression for frequency into the energy equation:
E = h * (c / λ)
We know that the energy required to remove one mole of electrons is 475 kJ (1 kJ = 1000 J) and we have Planck's constant (h) and the speed of light (c). We need to convert 475 kJ to joules:
475 kJ = 475 * 1000 J = 475,000 J
Now, we can solve for λ:
475,000 J = (6.626 x 10^(-34) J·s) * (3.00 x 10^8 m/s) / λ
Now, solve for λ:
λ = (6.626 x 10^(-34) J·s) * (3.00 x 10^8 m/s) / 475,000 J
λ ≈ 4.18 x 10^(-7) meters
So, the maximum wavelength of light capable of removing an electron from the surface of the solid metal is approximately 4.18 x 10^(-7) meters, or about 418 nanometers (nm). This falls within the ultraviolet part of the electromagnetic spectrum.