Question 193: Units , Dimensions and Error Analysis

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 :

Accepted Answer

V
0
$ \propto $ h
P
c
Q
G
R
I
S
[V
0
] = [M
1
L
2
T
Ã¢ÂÂ3
A
Ã¢ÂÂ1
]
[c] = [L
1
T
Ã¢ÂÂ1
]
[h] = [M
1
L
2
T
Ã¢ÂÂ1
]
[G] = [M
Ã¢ÂÂ1
L
3
T
Ã¢ÂÂ2
]
[I] = [A]
$ 	herefore $ [M
1
L
2
T
Ã¢ÂÂ3
A
Ã¢ÂÂ1
] =  [M
PÃ¢ÂÂR
L
2P+Q+3R
T
Ã¢ÂÂPÃ¢ÂÂQÃ¢ÂÂ2R
A
S
]
Comparing dimension of M, L, T, A, we get
P Ã¢ÂÂ R = 1 ; 2P + Q + 3R = 2
Ã¢ÂÂ P Ã¢ÂÂ Q Ã¢ÂÂ 2R = Ã¢ÂÂ 3 ; S = Ã¢ÂÂ 1
$ \Rightarrow $ P = 0, Q = 5, R = Ã¢ÂÂ1, S = Ã¢ÂÂ1
$ 	herefore $ V
0
$ \propto $ h
0
c
5
G
-1
A
-1

Answer

h
1/3
G
2/3
c
1/3
A
–1

Answer

h
0
c
5
G
-1
A
-1

Answer

h
2/3
c
5/3
G
1/3
A
–1

Answer

h
2
G
3/2
c
1/3
A
–1

Units , Dimensions and Error Analysis

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 :

Choose the correct answer: