Question

The wavelength associated with a moving particle depends upon power $p$ of its mass $m$, $q^{th}$ power of its velocity $v$ and $r^{th}$ power of Planck's constant $h$. Then the correct set of values of $p,q$ and $r$ is:-

• A. $p=1,q=-1,r=-1$
• B. $p=1,q=1,r=1$
• C. $p=-1,q=-1,r=-1$
• D. $p=-1,q=-1,r=1$

Answer 1

The correct option is C $p=-1,q=-1,r=-1$

Wavelength dimension $=\left[L\right]$

Mass Dimension $=\left[M\right]$

Velocity dimension $=\left[{LT}^{-1}\right]$

Planck constant dimension $=\left[{ML}^2{T}^{-1}\right]$

now,

$\left[L\right]=K{\left[M\right]}^a{\left[{LT}^{-1}\right]}^b{\left[{ML}^2{T}^{-1}\right]}^c$

$=K{\left[M\right]}^{(a+c)}{\left[L\right]}^{(b+2c)}{\left[T\right]}^{(b-c)}$

Compare $L.H.S$ to $R.H.S$

at $c=0$ ; $b+2c=1$ ; $-b-c=0$

$c=1$ ; $b=-1$ ; $a=-1$