The binding energy of electrons in a metal is 193 kJ/mol. What is the threshold frequency of the metal?

Verified step by step guidance

1. Understand that the binding energy given is the energy required to remove an electron from the metal surface, which is also known as the work function (\( \phi \)).
2. Convert the binding energy from kJ/mol to J per electron. Use the conversion factor: 1 kJ = 1000 J and Avogadro's number (\(6.022 \times 10^{23}\) mol\(^{-1}\)).
3. Use the formula for the work function in terms of frequency: \( \phi = h \nu_0 \), where \( h \) is Planck's constant (\(6.626 \times 10^{-34} \) J·s) and \( \nu_0 \) is the threshold frequency.
4. Rearrange the formula to solve for the threshold frequency: \( \nu_0 = \frac{\phi}{h} \).
5. Substitute the converted work function value and Planck's constant into the equation to find the threshold frequency.