Determine the longest wavelength of light required to remove an electron from a sample of potassium metal if the binding energy for an electron in potassium metal is 1.76 × 10³ kJ mol^-1. A) 147 nm B) 68.0 nm C) 113 nm D) 885 nm E) 387 nm

Question

Quizplus · Accepted Answer

The energy required to remove an electron from a metal is given by the binding energy. We can use the following formula to relate the binding energy to the longest wavelength of light required to remove an electron:

E = hc/λ - BE

where E is the energy of a photon with wavelength λ, h is Planck's constant, c is the speed of light, and BE is the binding energy. Solving for λ, we get:

λ = hc/(E - BE)

Substituting the given values, we get:

λ = (6.626 × 10^-34 J s) × (3.00 × 10^8 m/s) / ((1.76 × 10^3 J/mol) / (6.022 × 10^23 electrons/mol)) - (1.76 × 10^3 J/mol) / (6.022 × 10^23 electrons/mol)

λ = 68.0 nm

Therefore, the longest wavelength of light required to remove an electron from potassium metal is 68.0 nm. The answer is B.

Determine the Longest Wavelength of Light Required to Remove an Electron