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A dimensionless quantity is formed using the electronic charge e, the permittivity of free space ε₀, Planck's constant h, and the speed of light c. If the expression for the dimensionless quantity is eⁿε₀ᵅhᵝcᵞ, where n is a non-zero integer, what is the correct set of values for (α, β, γ, δ)?

1. (2n, −n, −n, −n)
2. (n, −n, −2n, −n)
3. (n, −n, −n, −2n)
4. (2n, −n, −2n, −2n)

Correct answer: (2n, −n, −n, −n)

Solution

The correct set of values for (α, β, γ, δ) is (2n, −n, −n, −n) because the expression eⁿε₀ᵅhᵝcᵞ must be dimensionless, which means that the exponents of the fundamental units must cancel out, leading to the given values of α, β, γ, and δ.

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