To calculate the phase constant of a wave with a skin depth of 2.5 units, we need to understand the relationship between skin depth and the phase constant.

1. Understanding Skin Depth:
Skin depth is a characteristic of electromagnetic waves that describes how deeply the wave penetrates into a conducting medium. It is denoted by the symbol δ and is defined as the distance at which the amplitude of the wave decreases to e^-1 (approximately 0.368) of its original value.

2. Skin Depth Formula:
The skin depth (δ) can be calculated using the formula:
δ = √(2/μσω),
where:
- δ is the skin depth,
- μ is the permeability of the medium,
- σ is the conductivity of the medium,
- ω is the angular frequency of the wave.

3. Relationship between Skin Depth and Phase Constant:
The phase constant (β) is related to the skin depth (δ) as follows:
β = 2π/λ = 2π/√(μσω),
where:
- β is the phase constant,
- λ is the wavelength of the wave.

4. Calculating the Phase Constant:
Given that the skin depth (δ) is 2.5 units, we can substitute this value into the skin depth formula and solve for β:
2.5 = √(2/μσω).

Rearranging the equation, we get:
μσω = (2/2.5)^2 = 16/25.

Now, substituting this value into the formula for β, we have:
β = 2π/√(μσω) = 2π/√(16/25) = 2π/(4/5) = 2π*(5/4) = 5π/2.

Therefore, the phase constant of the wave with a skin depth of 2.5 units is 5π/2, which can be simplified as 2.5π.

Hence, the correct answer is option D) 2/5.