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Multiple Choice
The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 kJ/mol. What wavelength (in nm) of light has sufficient energy per photon to dislodge an electron from the surface of sodium?
A
500 nm
B
218 nm
C
435 nm
D
350 nm
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Verified step by step guidance
1
First, understand that the energy required to dislodge electrons is given in kJ/mol. To find the energy per photon, convert this energy to joules per photon. Use the conversion factor: 1 kJ = 1000 J.
Next, calculate the energy per photon. Since 1 mole of photons contains Avogadro's number of photons (approximately 6.022 x 10^23), divide the total energy in joules by Avogadro's number to find the energy per photon.
Use the equation for the energy of a photon: E = h * c / λ, where E is the energy per photon, 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 λ is the wavelength in meters.
Rearrange the equation to solve for the wavelength: λ = h * c / E. Substitute the values for h, c, and the calculated energy per photon into this equation.
Finally, convert the wavelength from meters to nanometers by multiplying by 10^9, since 1 meter = 10^9 nanometers. Compare the calculated wavelength to the given options to determine which one is correct.