Question

The dimension of stopping potential $V_0$ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :

• A. $h ^{-2/3} c ^{-1/3} G ^{4/3} A ^{-1}$
• B. $h^{0} c^{5} G^{-1} A^{-1}$
• C. $h ^{2} G ^{3/2} c^{1/3} A^{-1}$
• D. $h ^{1/3} G ^{2/3} c ^{1/3} A ^{- 1}$

Answer 1

Answer: (B)

$v_{0}=h^{x}\,c^{y}\,G^{z}\,A^{w}$
$\frac{ML^{2}T^{-2}}{AT}=\left(ML^{2}T^{-1}\right)^{x}\left(LT^{-1}\right)\left(M^{-1}L^{3}T^{-2}\right)^{z}A^{w}$
$\Rightarrow w=-1$
$\left(x - z = 1\right)$
$2x + y + 3x = 2$
$\frac{-x-y-2z=-3}{2x=0}$
$x=0$
$z=-1
y=5$
$\Rightarrow v_{0}=h^{0}c^{5}G^{-1}A^{-1}$