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1.Units, Dimensions and Measurement
hard
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 .......
A$\left[ M ^{0} L ^{0} T ^{0}\right]$
B$\left[ L C ^{-1}\right]$
C$\left[ M L T ^{-1}\right]$
D$\left[ M L T ^{0}\right]$
(JEE MAIN-2021)
Solution
$F =\frac{1}{4 \pi \epsilon_{0}} \frac{ e ^{2}}{ r ^{2}}$
$E =\frac{ hc }{\lambda}$
$\left[\frac{ e ^{2}}{4 \pi \varepsilon_{0}} \times \frac{1}{ hc }\right]=\frac{ Fr ^{2}}{ E \lambda}=\left( M ^{0} L ^{0} T ^{0}\right)$
$E =\frac{ hc }{\lambda}$
$\left[\frac{ e ^{2}}{4 \pi \varepsilon_{0}} \times \frac{1}{ hc }\right]=\frac{ Fr ^{2}}{ E \lambda}=\left( M ^{0} L ^{0} T ^{0}\right)$
Standard 11
Physics
