# The dimension of stopping potential

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:

1. $h^{1 / 3} G^{2 / 3} c^{1 / 3} A^{-1}$

2. $h^{2 / 3} c^{5 / 3} G^{1 / 3} A^{-1}$

3. $h^{-2 / 3} e^{-1 / 3} G^{4 / 3} A^{-1}$

4. None of these

Correct Option: , 4

Solution:

(4)

Stopping potential $\left(V_{0}\right) \propto h^{x} I^{y} G^{Z} C^{r}$

Here, $h=$ Planck's constant $=\left[M L^{2} T^{-1}\right]$

$I=$ current $=[A]$

$G=$ Gravitational constant $=\left[M^{-1} L^{3} T^{-2}\right]$

and $c=$ speed of light $=\left[L T^{-1}\right]$

$V_{0}=$ potential $=\left[M L^{2} T^{-3} A^{-1}\right]$

$\therefore\left[M L^{2} T^{-3} A^{-1}\right]=\left[M L^{2} T^{-1}\right]^{\mathrm{x}}[A]^{\mathrm{y}}\left[M^{-1} L^{3} T^{-2}\right]^{\mathrm{z}}\left[L T^{-1}\right] r$

$M^{x-z} ; L^{2 x+3 z+r} ; T^{-x-2 z-r} ; A^{y}$

Comparing dimension of $\mathrm{M}, \mathrm{L}, \mathrm{T}, \mathrm{A}$, we get

$y=-1, x=0, z=-1, r=5$

$\therefore \quad V_{0} \propto h^{0} I^{-1} G^{-1} C^{5}$