If e is the electronic charge, c is the speed


If $e$ is the electronic charge, $c$ is the speed of light in free space and $\mathrm{h}$ is Planck's constant,

the quantity $\frac{1}{4 \pi \varepsilon_{0}} \frac{|\mathrm{e}|^{2}}{h c}$ has dimensions of :

  1. $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$

  2. $\left[\mathrm{L} \mathrm{C}^{-1}\right]$

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

  4. $[\mathrm{M} \mathrm{L} \mathrm{T}$ ]

Correct Option: 1


$\mathrm{F}=\frac{1}{4 \pi \epsilon_{0}} \frac{\mathrm{e}^{2}}{\mathrm{r}^{2}}$


$\left[\frac{\mathrm{e}^{2}}{4 \pi \varepsilon_{0}} \times \frac{1}{h c}\right]=\frac{\mathrm{Fr}^{2}}{\mathrm{E} \lambda}=\left(\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right)$

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