Question

The dimensions of the quantity $hv/c$, where $h$ is planck's constant, $v$ is the frequency and $c$ is the velocity of light is

• A. $\left[M{L}^{-1}\right]$
• B. $\left[ML{T}^{-1}\right]$
• C. $\left[ML{T}^{-2}\right]$
• D. $\left[M{L}^2{T}^2\right]$

Answer 1

Answer: (B)

$\left[ML{T}^{-1}\right]$

By de Broglie hypothesis, wavelength $\lambda =\frac{h}{p}$ or $\frac{c}{\nu }=\frac{h}{p}$ or $p=\frac{h\nu }{c}$

Thus, the given quantity $h\nu /c$ represents the momentum $p$.

We know that the dimension of momentum is $\left[p\right]=\left[ML{T}^{-1}\right]$