Q. 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) $p = - 1,q = - 1,r = 1$
Explanation
$\lambda = m^{p}v^{q}h^{r}$ $\left\lbrack M^{0}LT^{0} \right\rbrack = \left\lbrack M^{p} \right\rbrack\left\lbrack LT^{- 1} \right\rbrack^{q}\left\lbrack ML^{2}T^{- 2} \right\rbrack^{r}$ $\left\lbrack M^{0}LT^{0} \right\rbrack = \lbrack M^{p + r}L^{q + 2r}T^{- q - r}\rbrack$ $\therefore\ \ \ p + r = 0,q + 2r = 1, - q - r = 0$ After solving we get $p = - 1,q = - 1,r = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.