Question

The wavelength associated with $a$ moving particle depends upon $p^{th}$ power of its mass $m,q^{th}$ power of its velocity $v$ and rth power of Planck’s constant h. Then the sum of values of $p,q$ and $r$ is $-K.$ Find the value of $K$?

Answer 1

Answer: 1

Given $\lambda =k{m}^p{v}^p{h}^k$. The dimensions of right-hand rule and left-hand side terms should be equal.
So $[M^{0}L{T}^0]=[M{]}^p[L{T}^{-1}{]}^q[M{L}^2{T}^{-1}{]}^r$
or $[M^{0}L{T}^0]=[M^{p+r}][L^{q+2r}][T^{-q-r}]$
Now, compare powers of $M,L$ and $T,$ we get
$p+r=0...(i)$
$q+2r=1...(ii)$
$-q-r=0...(iii)$
After solving p $=-1,q=-1$ and $r=1$ putting these values, we get