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)

$v_0=h^x{c}^y{G}^z{A}^w$
$\frac{M{L}^2{T}^{-2}}{AT}={\left(M{L}^2{T}^{-1}\right)}^x\left(L{T}^{-1}\right){\left(M^{-1}{L}^3{T}^{-2}\right)}^z{A}^w$
$\Rightarrow w=-1$
$\left(x-z=1\right)$
$2x+y+3x=2$
$\frac{-x-y-2z=-3}{2x=0}$
$x=0$
$z=-1<br/>y=5$
$\Rightarrow v_0=h^0{c}^5{G}^{-1}{A}^{-1}$