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Question

The dimension of stopping potential V0 in photoelectric effect in units of Planck's constant h, speed of light c, Gravitational constant G and ampere A is:

A
h1/3G2/3c1/3A1
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B
h2/3G5/3c1/3A1
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C
h4/3G2/3c1/3A1
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D
h0G1c5A1
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Solution

The correct option is D h0G1c5A1
Let, the dimensional formula for,

Stopping potential (V0)hxAyGzcr

Here,
hPlanck's constant=[ML2T1]
A current=[A]
GGravitational constant=[M1L3T2]
and cspeed of light=[LT1]

V0=potential=[ML2T3A1]

Using dimensional analysis,

[ML2T3A1]=[ML2T1]x[A]y[M1L3T2]z[LT1]r

[ML2T3A1]=MxzL2x+3z+rTx2zrAy
Comparing and solving the dimension of M,L,T,A, we get,

y=1,x=0,z=1,r=5
V0h0A1G1c5

Hence, option (D) is correct.

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