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
A. (2 n,-n,-n,-n)
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
Related: Physics — Units and Dimensions · All PYQ Banks