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Question:

If the capacitance of a nano capacitor is measured in terms of a unit μ made by combining the electronic charge 'e', bohr radius 'a0', Planck's constant 'h' and speed of light 'c' then which of the following relation is possible?

μ=e2a0hc

μ=e2hca0

μ=hce2a0

μ=e2cha0

Solution:

e²/4πε₀hc is a dimensionless constant
Dimension of ε₀ has dimension of e²/hc
Capacitance C has dimension of ε₀
Adi.e. dim[ε₀][length] ∴ capacitance μ can be expressed in units of ε₀ × length
Bohr's radius a₀ has unit of length.
∴ μ=e²a₀hc