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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
If e is the electronic charge, $c$ is the speed of light in free space and $h$ is Planck's constant, the quantity $\frac{1}{4 \pi \varepsilon_{0}} \frac{| e |^{2}}{h c}$ has dimensions of .......
  • ✓
    $\left[ M ^{0} L ^{0} T ^{0}\right]$
  • B
    $\left[ L C ^{-1}\right]$
  • C
    $\left[ M L T ^{-1}\right]$
  • D
    $\left[ M L T ^{0}\right]$
✓

Answer

Correct option: A.
$\left[ M ^{0} L ^{0} T ^{0}\right]$
a
$F =\frac{1}{4 \pi \in_{0}} \frac{ e ^{2}}{ r ^{2}}$

$E =\frac{ hc }{\lambda}$

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

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