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JEE Main202127 Aug 2021Evening ShiftPhysicsUnits and DimensionsActual

Match List- I with List- II . List- I List- II a R H (Rydberg constant) i kg m - 1 s - 1 b h (Planck's constant) ii kg m 2 s - 1 c μ B (Magnetic field energy density) iii m - 1 d η (coefficient of viscosity) iv kg m - 1 s - 2 Choose the most appropriate answer from the options given below:

Options

  1. A( a ) -( iv ),   ( b )-( ii ),   ( c )-( i ),   ( d )-( iii )
  2. B( a ) - ( ii ) ,   ( b ) - ( iii ) ,   ( c ) - ( iv ) ,   ( d ) - ( i )
  3. C( a ) - ( iii ) ,   ( b ) - ( ii ) ,   ( c ) - ( iv ) ,   ( d ) - ( i )
  4. D( a ) - ( iii ) ,   ( b ) - ( ii ) ,   ( c ) - ( i ) ,   ( d ) - ( iv )

Correct answer

C. ( a ) - ( iii ) ,   ( b ) - ( ii ) ,   ( c ) - ( iv ) ,   ( d ) - ( i )

Step-by-step solution

The relation between wavelength and the principal quantum number is, 1 λ = R 1 n 1 2 - 1 n 2 2 , for hydrogen-like atom, so the unit to Rydberg constant is, m - 1 . Now recall the formula of energy of a photon in terms of frequency, E = h ν , it means, h = E ν = kg   m 2   s - 2 s - 1 = kg   m 2   s - 1 . The coefficient of viscosity, η = F A × d v d z = kg   m   s - 2   m m 2 × m   s - 1 = kg   m - 1   s - 1 . Energy density is defined

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