The dimension of stopping potential \(\mathrm{V}_{0}\) in photoelectric effect in units of Planck's constant \(h\), speed of light \(c\) and Gravitational constant \(G\) and ampere \(A\) is

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Correct Answer

(D) \(\mathrm{h}^{0} \mathrm{c}^{5} \mathrm{G}^{-1} \mathrm{A}^{-1}\)

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Detailed explanation

\(\mathrm{v}_{0}=\mathrm{h}^{\mathrm{x}} \mathrm{c}^{\mathrm{y}} \mathrm{G}^{\mathrm{z}} \mathrm{A}^{\mathrm{w}}\)

\(\frac{\mathrm{ML}^{2} \mathrm{T}^{-2}}{\mathrm{AT}}=\left(\mathrm{ML}^{2} \mathrm{T}^{-1}\right)^{\mathrm{x}}\left(\mathrm{LT}^{-1}\right)^{\mathrm{y}}\left(\mathrm{M}^{-1} \mathrm{L}^{3} \mathrm{T}^{-2}\right)^{\mathrm{z}} \mathrm{A}^{\mathrm{w}}\)

\(\Rightarrow \mathrm{w}=-1\)

\((\mathrm{x}-\mathrm{z}=1)\)

\(-\mathrm{x}-\mathrm{x}=1-2 \mathrm{z}=2\)

\(-\mathrm{x}-\mathrm{y}-2 \mathrm{z}=-3\)

\(\mathrm{x}-\frac{1}{2} \mathrm{x}=0\)

\(\mathrm{x}=0\)

\(\mathrm{x}=-1\)

\(2 \times 0+\mathrm{y}+3 \mathrm{x}-1=2\)

\(y=5\)

\(\Rightarrow \mathrm{v}_{0}=\mathrm{h}^{0} \mathrm{c}^{5} \mathrm{G}^{-1} \mathrm{A}^{-1}\)