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Sodium is a soft metal with a relatively low work function. Light corresponding to 476 kJmol−1 was shone on the sodium metal, and the electrons detected had a velocity of 9.57×105ms−1. What is the work function of sodium metal based on this data? The mass of an electron is 9.11×10−31kg.

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Based on the data given, the work function of sodium metal is equal to [tex]7.91 \times 10^{-19}\;Joules[/tex].

Given the following data:

  • Mass of an electron = [tex]9.11\times10^{-31}\;kg[/tex].
  • Photo electric work function = 476 kJ/mol.
  • Velocity of electrons = [tex]9.57\times10^{5}\;m/s[/tex]

Avogadro constant = [tex]6.02 \times 10^{23}[/tex]

To determine the work function of sodium metal based on this data:

Mathematically, the photoelectric effect is given  by the formula:

[tex]K.E = hf - BE_i[/tex]

Where:

  • K.E represents the maximum kinetic energy of the ejected electron.
  • f is photon frequency.
  • h is Planck constant ([tex]6.626 \times 10^{-34}\;J.s[/tex]).
  • [tex]BE_i[/tex] is the work function of the material.

However, since we were given the photo electric work function of light that was shone on the sodium metal, we would calculate the work function of sodium metal as follows:

[tex]\phi = \frac{Photo \;electric\; work \;function}{Avoadro's\;number}[/tex]

[tex]\phi = \frac{476 \times 10^3}{6.02 \times 10^{23}} \\\\\phi = 7.91 \times 10^{-19}\;Joules[/tex]

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