Question

Energy of a photon is given by $E= hv$ where $v$ is the number of vibrations per second and $h$ is Planck's constant. Dimensions of Planck's constant are

• A. $\left[ M ^{0}\, L ^{0}\, T ^{0}\right]$
• B. $\left[ ML ^{2} \,T ^{-1}\right]$
• C. $\left[ ML ^{2} \,T ^{-2}\right]$
• D. $\left[ ML ^{2} \,T ^{-3}\right]$

Answer 1

Answer: (B)

$E=h v$ or $h=\frac{E}{v}$
So, dimensions of $h=\frac{\text { dimensions of } E}{\text { Dimensions of } v}$
$=\frac{\left[M L^{2} \,T^{-2}\right]}{\left[M^{0} \, L^{0} \, T^{-1}\right]}=\left[M L^{2} \, T^{-1}\right]$
$=\frac{\left[M L^{2} \, T^{-2}\right]}{\left[M^{0} \,L^{0} \, T^{-1}\right]}=\left[M L^{2} \, T^{-1}\right]$