Multiple Choice
When sunlight strikes a metal surface, what can happen to an electron according to the photoelectric effect?
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9. Quantum Mechanics
Photoelectric Effect
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An ultraviolet photon with a wavelength of 320 nm strikes a metal surface. The emitted electron has a kinetic energy of 3.0 x 10-2 eV. What is the binding energy of the electron in kJ/mol? 1 electron volt (eV) = 1.602 x 10-19 J.
A
320 kJ/mol
B
370 kJ/mol
C
450 kJ/mol
D
405 kJ/mol
Verified step by step guidance1
First, convert the wavelength of the ultraviolet photon from nanometers to meters. Since 1 nm = 1 x 10^-9 m, the wavelength in meters is 320 nm x 1 x 10^-9 m/nm.
Next, use the equation for the energy of a photon: E = \( \frac{hc}{\lambda} \), where h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and \( \lambda \) is the wavelength in meters. Substitute the values to find the energy of the photon in joules.
Convert the kinetic energy of the emitted electron from electron volts to joules using the conversion factor: 1 eV = 1.602 x 10^-19 J. Multiply the kinetic energy in eV by this factor to get the energy in joules.
Calculate the binding energy of the electron by subtracting the kinetic energy of the electron (in joules) from the energy of the photon (in joules). This gives the binding energy in joules per electron.
Finally, convert the binding energy from joules per electron to kJ/mol. Use Avogadro's number (6.022 x 10^23 mol^-1) to convert from energy per electron to energy per mole, and then convert joules to kilojoules by dividing by 1000.
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