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] = h^a 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 A^b [M^-1 L³ T^-2 ]^c [LT ^-1]^d 

[ML² T^-3 A^-1] = [M^a-c L^2a+3c+d T^-a-2c-d A^b ]

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