an x-ray photon of wavelength 0.989nm stricks a surface. the emitted electron has a kinetic energy of 969 eV.what is the binding energy of the electron in kj/mol?
To determine the binding energy of the electron in kJ/mol, we need to follow a series of steps:
Step 1: Calculate the energy of the incident X-ray photon.
The energy of a photon can be calculated using the equation: E = h * c / λ, where E is energy, h is Planck's constant (6.62607004 × 10^-34 J⋅s), c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength of the photon.
Converting the given wavelength from nm to meters:
0.989 nm * (1 m / 10^9 nm) = 9.89 × 10^-10 m
Calculating the energy of the incident X-ray photon:
E = (6.62607004 × 10^-34 J⋅s * 2.998 × 10^8 m/s) / (9.89 × 10^-10 m)
E ≈ 1.99920384 × 10^-16 J
Step 2: Convert the energy of the incident X-ray photon to electron volts (eV).
1 eV is equal to 1.60218 × 10^-19 J.
Converting the energy from joules to electron volts:
E (eV) = (1.99920384 × 10^-16 J) / (1.60218 × 10^-19 J/eV)
E (eV) ≈ 1,247.612823 eV
Step 3: Calculate the binding energy of the electron.
Binding energy is the difference between the energy of the incident photon and the kinetic energy of the emitted electron.
Binding energy = Energy of incident photon - Kinetic energy of electron
Binding energy ≈ 1,247.612823 eV - 969 eV
Binding energy ≈ 278.612823 eV
Step 4: Convert the binding energy from electron volts to kilojoules per mole (kJ/mol).
One mole (mol) of electrons would contain Avogadro's number of electrons (6.022 × 10^23).
Converting the binding energy from electron volts to joules:
Binding energy (J) = (278.612823 eV) * (1.60218 × 10^-19 J/eV)
Binding energy (J) ≈ 4.466499913 × 10^-17 J
Calculating the binding energy in kJ/mol:
Binding energy (kJ/mol) = (4.466499913 × 10^-17 J) / (6.022 × 10^23 mol^-1)
Binding energy (kJ/mol) ≈ 0.07415 kJ/mol
Therefore, the binding energy of the electron is approximately 0.07415 kJ/mol.