Answer :

The threshold frequency of the metal is approximately 2.92×10¹⁹ Hz.

The threshold frequency of the metal can be calculated as shown below:

Explanation:Binding energy (BE) of electrons in a metal = 193 kJ/mol

Threshold frequency, f₀ = ?

Planck’s constant, h = 6.626 × 10⁻³⁴ J s

We know that the binding energy of the electrons in the metal is given as:E = hf …..(1)

where E is the binding energy of electrons, h is Planck’s constant, and f is the frequency of light incident on the metal.

The equation (1) can be written as:f = E/h …..(2)

From equation (2), we have the frequency of light f=f0 + c / λ

where f0 is the threshold frequency of the metal, c is the speed of light, and λ is the wavelength of the light incident on the metal.

Now, substituting the values of E and h in equation (2),

we get:f₀ = E/h = (193 × 10³)/(6.626 × 10⁻³⁴)=2.915×10¹⁹ Hz≈2.92×10¹⁹ Hz

Hence, the threshold frequency of the metal is approximately 2.92×10¹⁹ Hz.

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