Units & Dimensions

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82 of 149

Question 82 of 149

Match List I with List II List I List II A.A. Planck's constant (h)\left(h\right) I.I. [M1L2T−2]\left[{M}^{1}{L}^{2}{T}^{-2}\right] B.B. Stopping potential (Vs)\left({V}_{s}\right) II.II. [M1L1T−1]\left[{M}^{1}{L}^{1}{T}^{-1}\right] C.C. Work function (ϕ)\left(\phi \right) III.III. [M1L2T−1]\left[{M}^{1}{L}^{2}{T}^{-1}\right] D.D. Momentum (p)\left(p\right) IV.IV. [M1L2T−3A−1]\left[{M}^{1}{L}^{2}{T}^{-3}{A}^{-1}\right]

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Answer: (B) A−III,B−IV,C−I,D−IIA-III,B-IV,C-I,D-II

The dimension of momentum is,
p=[M1L1T−1]p=\left[{M}^{1}{L}^{1}{T}^{-1}\right]
From de Broglie equation,
hp=λ\dfrac{h}{p}=\lambda
[h]=[p][λ]=[ML2T−1][h]=[p]\left[\lambda \right]=\left[M{L}^{2}{T}^{-1}\right]
The stopping potential is related to maximum kinetic energy of emitted electron as
Vs=KEmaxe{V}_{s}=\dfrac{K{E}_{max}}{e}
=[ML2T−2][AT]=[ML2T−3A−1]=\dfrac{\left[{ML}^{2}{T}^{-2}\right]}{\left[AT\right]}=\left[{ML}^{2}{T}^{-3}{A}^{-1}\right]
From Einstein's photoelectric equation, the work function ϕ\phi has dimensions of energy
[ϕ]=[ML2T−2]\left[\phi \right]=\left[{ML}^{2}{T}^{-2}\right]

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