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The dimension of stooping potential V(0)...

The dimension of stooping potential `V_(0)` in photoelectric effect In units of Planck's constant 'h', spee of light 'c' and Gravitional constant 'G' and ampere A is:

A

`h^(-2//3) c^(-1//3) G^(4//3) A^(-1)`

B

`h^(2//3) c^(5//3) G^(1//3) A^(-1)`

C

`h^(1//3) c^(2//3) G^(1//3) A^(-1)`

D

`(h)^(0) (c)^(5) (G)^(-1) (A)^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
D
`V_0= h^(x) c^(y)G^(z) A^(w)`
`(ML^(2)T^(-2))/(AT)=(ML^(2) T^(-1))^(x)(LT^(-1))^(y)(M^(-1)L^3 T^(-2))^(z)(A)^(w)`
`M^(1)L^(2) T^(-3) A^(-1)= M^(x-z) L^(2x +y+3z)T^(-x-y-2z)A^(w)`
on comparing we get,
`w=-1 , " " x-z=1`
`2x + y + 3z = 2, x-y-2z = -3`
On solving we get, `x = 0, y=5 and z=-1`
`V_0 = (h)^(0)(c)^(5) (G)^(-1) (A)^(-1)`
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