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JEE Main 202127 AugustEvening Shift
Exam
JEE Main
Year
2021
Date
27 August
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2021 · 27 August · Evening Shift · Physics · Units and Dimensions

Match List- (I) with List-(II) . List- (I) List-(II) a R _ H...

Match List-(I)\left(I\right) with List-\left(II\right).</p><tableborder="1"cellpadding="1"cellspacing="1"style="width:500px;"><tbody><tr><td></td><td>List−.</p><table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"> <tbody> <tr> <td> </td> <td>List-\left(I\right)</td><td></td><td>List−(II)</td> <td> </td> <td>List-\left(II\right) a RH{R}_{H} (Rydberg constant) i kgm−1s−1kg{m}^{- 1}{s}^{- 1} b hh (Planck's constant) ii kgm2s−1kg{m}^{2}{s}^{- 1} c μB{\mu}_{B} (Magnetic field energy density) iii m−1{m}^{- 1} d ηη (coefficient of viscosity) iv kgm−1s−2kg{\text{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)( a ) -( iv ), ( b )-( ii ), ( c )-( i ), ( d )-( iii )
  2. B(a)−(ii),(b)−(iii),(c)−(iv),(d)−(i)( a ) - ( ii ) , ( b ) - ( iii ) , ( c ) - ( iv ) , ( d ) - ( i )
  3. C(a)−(iii),(b)−(ii),(c)−(iv),(d)−(i)( a ) - ( iii ) , ( b ) - ( ii ) , ( c ) - ( iv ) , ( d ) - ( i )
  4. D(a)−(iii),(b)−(ii),(c)−(i),(d)−(iv)( a ) - ( iii ) , ( b ) - ( ii ) , ( c ) - ( i ) , ( d ) - ( iv )

Correct answer

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

Step-by-step solution

The relation between wavelength and the principal quantum number is, 1λ=R(1(n1)2−1(n2)2)\dfrac{1}{\lambda} = R\left(\dfrac{1}{{\left({n}_{1}\right)}^{2}} - \dfrac{1}{{\left({n}_{2}\right)}^{2}}\right), for hydrogen-like atom, so the unit to Rydberg constant is, m−1{m}^{- 1}.

Now recall the formula of energy of a photon in terms of frequency, E=hνE = hν, it means, h=Eν=kgm2s−2s−1=kgm2s−1h = \dfrac{E}{ν} = \dfrac{kg{m}^{2}{s}^{- 2}}{{s}^{- 1}} = kg{m}^{2}{s}^{- 1}.

The coefficient of viscosity,
η=FA×dvdz=kgms−2mm2×ms−1=kgm−1s−1.η = \dfrac{F}{A \times \dfrac{dv}{dz}} = \dfrac{kgm{s}^{- 2}m}{{m}^{2} \times m{s}^{- 1}} = kg{m}^{- 1}{s}^{- 1} .

Energy density is defined as, EV=kgm2s−2m3=kgm−1s−2\dfrac{E}{V} = \dfrac{kg{m}^{2}{s}^{- 2}}{{m}^{3}} = kg{m}^{- 1}{s}^{- 2}.

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