CBSE Class 11-science Answered
The dimension of the stopping potential Vo in terms of Planck's constant(h), gravitational constant(G), speed of light (C) and Ampere(A) is,
Dimension of [V] = ha A b G c C d
Here,
a,b, c, d -> integers
We know,
Energy of photon is
E = h/ν
h -> Planck's constant
ν -> frequency
thus,
h = E/ν
Dimension of E =[ M L2 T-2 ]
dimension of v = [T-1]
Thus, dimensions of Planck's constant, h = [ML2T-1]
Dimensions of Gravitational force
G = [M-1 L3 T-2]
The actual dimensions of stopping potential is
V = [ML2 T-3 A-1]
For calculating the dimensions of stopping potential in terms of the given quantities,
[ML2 T-3 A-1]= [ML2T-1]a Ab [M-1 L3 T-2 ]c [LT -1]d
[ML2 T-3 A-1] = [Ma-c L2a+3c+d T-a-2c-d Ab ]
Comparing both the sides we get,
a - c = 1
2a + 3c+ d = 2
-a -2c -d = -3
b = -1
On solving,
c = -1
a = 0
d = 5
b= -1
Thus,
Dimensions of the stopping potential is,
V0 = h0 A-1 G-1 C5