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the dimension of stopping potential vo in photoelectric effect in units of plank's constant 'h',speed of light 'c' and gravitational constant 'G' and ampereA
Asked by derhebha955 | 03 Apr, 2024, 09:03: AM

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]

[ML2 T-3 A-1] = [Ma-c L2a+3c+d T-a-2c-d A]

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

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