Question

the wavelength lambda associated with a moving particle depends upon its mass m velocity v and planck's constant h.show dimensionally the relation between them???

Answer 1

wavelength dimension=[L]
mass dimension=[M]
velocity dimension= [LT^-1]
plank constant dimension=[ML^2T^-1]
now
[L]=k [M]^a [LT^-1] ^b [ML^2T^-1] ^c
=k [M]^(a+c)[L]^(b+2c)[T]^(-b-c)
compare LHS to RHS
a+c=0
b+2c=1
-b-c=0
so
c=1
b=-1
a=-1
hence
lemda=k .plank constant/(mass. velocity)

Answer 2

$\textbf{Answer is in Attachment !}$