If e is the electronic charged, c is the speed of light in free space

Question:

If e is the electronic charged, $\mathrm{c}$ is the speed of light in free space and $\mathrm{h}$ is planck's constant, the quantity $\frac{1}{4 \pi \varepsilon_{0}} \frac{|e|^{2}}{\mathrm{hc}}$ has dimensions of:

  1. $\left[\mathrm{LC}^{-1}\right]$

  2. $\left[M^{0} L^{0} T^{0}\right]$

  3. $\left[M L T^{0}\right]$

  4. $\left[M L T^{-1}\right]$


Correct Option: , 2

Solution:

(2)

Given $e=$ electronic charge $\mathrm{c}=$ speed of light in free space $\mathrm{h}=$ planck's constant $\frac{1}{4 \pi e_{0}} \frac{e^{2}}{h c}=\frac{k e^{2}}{h c} \times \frac{\lambda^{2}}{\lambda^{2}}$

$=\frac{F \times \lambda}{E}$

$=\frac{E}{E}$

$=$ dimensionless $=\left[M^{0} L^{0} T^{0}\right]$

Leave a comment