An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE = 1/2 mv²; 1 electron volt (eV) = 1.602×10^–19 J]

Verified step by step guidance

1. Convert the wavelength of the X-ray photon from nanometers to meters by using the conversion factor: 1 nm = 1 x 10^{-9} m.
2. Calculate the energy of the X-ray photon using the formula E = \frac{hc}{\lambda}, where h is Planck's constant (6.626 x 10^{-34} J\cdot s) and c is the speed of light (3.00 x 10^8 m/s).
3. Convert the kinetic energy of the emitted electron from electron volts (eV) to joules (J) using the conversion factor: 1 eV = 1.602 x 10^{-19} J.
4. Determine the binding energy of the electron by subtracting the kinetic energy (in joules) from the energy of the X-ray photon (in joules).
5. Convert the binding energy from joules to kilojoules per mole by using Avogadro's number (6.022 x 10^{23} mol^{-1}) and the conversion factor: 1 kJ = 1000 J.

Key Concepts

Photoelectric Effect

The photoelectric effect describes the phenomenon where electrons are emitted from a material when it absorbs light or electromagnetic radiation, such as X-rays. The energy of the incoming photon must exceed the binding energy of the electrons in the material for them to be released. The kinetic energy of the emitted electrons can be calculated by subtracting the binding energy from the energy of the incoming photon.

Energy of a Photon

The energy of a photon is inversely related to its wavelength and can be calculated using the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. In this question, the wavelength of the X-ray photon is given, allowing us to determine its energy, which is crucial for calculating the binding energy of the emitted electron.

Conversion of Energy Units

In this problem, it is necessary to convert energy units from electron volts (eV) to kilojoules per mole (kJ/mol). The conversion factor is 1 eV = 1.602 x 10^-19 J, and to convert joules to kilojoules, one divides by 1000. Additionally, to convert from energy per particle to energy per mole, Avogadro's number (6.022 x 10^23 mol^-1) is used, which is essential for expressing the binding energy in the desired units.