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 h0G−1c5A−1 Let, the dimensional formula for, Stopping potential (V0)∝hxAyGzcr Here, h→Planck's constant=[ML2T−1] A→ current=[A] G→Gravitational constant=[M−1L3T−2] and c→speed of light=[LT−1] V0=potential=[ML2T−3A−1] Using dimensional analysis, [ML2T−3A−1]=[ML2T−1]x[A]y[M−1L3T−2]z[LT−1]r [ML2T−3A−1]=Mx−zL2x+3z+rT−x−2z−rAy Comparing and solving the dimension of M,L,T,A, we get, y=−1,x=0,z=−1,r=5 ∴V0∝h0A−1G−1c5 Hence, option (D) is correct.

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