The wavelength associated with a moving particle depends upon pth power of its mass m, qth power of its velocity v and rth power of Planck’s constant h. Then the correct set of values of p, q and r is

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p = 1, q = 1, r = 1

p = 1, q = -1, r = 1

p = -1, p = -1, r = -1

p = -1, q = -1, r = 1

answer is D.

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Detailed Solution

$λ = m^{p} v^{q} h^{r}$

$[M^{0} L T^{0}] = [M^{p}] {[L T^{- 1}]}^{q} {[M L^{2} T^{- 1}]}^{r}$

$[M^{0} L T^{0}] = [M^{p + r} L^{q + 2 r} T^{- q - r}]$

$∴ p + r = 0, q + 2 r = 1, - q - r = 0$

After solving, we get

p = -1,q = -1,r =1

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