Final answer:
To find the wavelength of light capable of ejecting an electron from sodium metal, we convert the energy required to joules per electron and use Planck's equation, yielding a wavelength of 435 nm.
Step-by-step explanation:
The student's question pertains to the photoelectric effect as it applies to sodium metal. The energy required to dislodge electrons from sodium is given as 275 kJ/mol. To find the wavelength of light with enough energy to dislodge an electron from the surface of sodium, we utilize the photoelectric effect equation and Planck's equation.
First, we convert the energy from kJ/mol to joules (J) for a single electron using Avogadro's number:
E = (275 kJ/mol) × (1,000 J/kJ) / (6.022×10²23 mol²1) = 4.57×10²19 J
Next, we use Planck's equation which relates energy (E) and wavelength (λ) as E = h×c/λ, where h is Planck's constant (6.626×10²34 J·s) and c is the speed of light (3.00×10²8 m/s).
Rearranging the equation to solve for the wavelength, we get:
λ = h×c/E
Thus:
λ = (6.626×10²34 J·s) × (3.00×10²8 m/s) / (4.57×10²19 J)
λ = 4.35×10²7 m or 435 nm
This is the wavelength of light required to dislodge an electron from sodium via the photoelectric effect.