A dimensionless quantity is constructed in terms of electronic charge e , permittivity of free space ₀ , Planck's constant h and speed of light c . If the dimensionless quantity is written as e^ ₀^ h^ c^ and n is a non-zero integer, then ( , , , ) is given by

Step-by-step solution

For the quantity to be dimensionless aligned & e ^ ₀^ h ^ c ^ d = M ^0 ~L ^0 ~T ^0 ~A ^0 & ( AT )^ ( M ⁻¹ ~L ⁻³ ~T ^4 ~A ^2 )^ ( ML ^2 ~T ⁻¹ )^ ( LT ⁻¹ )^ = A ^0 M ^0 ~L ^0 ~T ^0 & +2 =0, +4 - - =0,- + =0 ~ &~-3 +2 + =0 & =-2 , = ~ &~ = aligned Option (1) satisfies the given condition