Understanding the Concepts

* Binding Energy: The binding energy is the minimum amount of energy required to remove an electron from a metal surface.

* Threshold Frequency: The minimum frequency of light that can cause photoemission (the ejection of electrons from a metal surface).

* Photoelectric Effect: The phenomenon where light can knock electrons out of a metal.

Equations

* Binding Energy (E) and Threshold Frequency (ν): E = hν

* Where:

* E is the binding energy (in Joules)

* h is Planck's constant (6.626 x 10⁻³⁴ J s)

* ν is the threshold frequency (in Hz)

Calculations

1. Convert Binding Energy to Joules:

* 178 kJ/mol = 178,000 J/mol

* Divide by Avogadro's number (6.022 x 10²³ atoms/mol) to get energy per atom:

178,000 J/mol / 6.022 x 10²³ atoms/mol = 2.96 x 10⁻¹⁹ J/atom

2. Calculate Threshold Frequency:

* Rearrange the equation: ν = E/h

* Plug in the values: ν = (2.96 x 10⁻¹⁹ J) / (6.626 x 10⁻³⁴ J s)

* Calculate: ν ≈ 4.46 x 10¹⁴ Hz

Answer

The threshold frequency for this metal is approximately 4.46 x 10¹⁴ Hz.