The wavelength `lambda` associated with a moving particle depends upon its mass (m) velocity (v) and Planck's constant 'h'. Show dimensionally that `lambda prop (h)/(mv)`.

Explanation

Let `lambda prop m^(a)v^(b)h^(c )implieslambda=km^(a)v^(b)h^(c )`………………(i)
Substituting the dimensional formulae of various physical quantities, we have
`L=M^(a)(LT^(-1))^(b)(ML^(2)T^(-1))^(c )`
or `L=M^(a+c)L^(b+2c)T^(-b-c)`
Comparing the dimension of mass, length and time, we have
`a+c=0impliesa=-c` .............(ii)
`b+2c=1` .........(iii)
and `-b-c=0impliesc=-b` (iv)
Substituting (iv) in (iii), we get `1=b-2bimpliesb=-1`
Therefore `c=1` , hence `a=-1`
Substituting in (i), we get `lambda=hm^(-1)v^(-1)` or `lambda prop (h)/(mv)`.