JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
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 \(\left[ M L T ^{0}\right]\)
Answer & Solution
Correct Answer
(A) \(\left[ M ^{0} L ^{0} T ^{0}\right]\)
Step-by-step Solution
Detailed explanation
\(F =\frac{1}{4 \pi \epsilon_{0}} \frac{ e ^{2}}{ r ^{2}}\) \(E =\frac{ hc }{\lambda}\) \(\left[\frac{ e ^{2}}{4 \pi \varepsilon_{0}} \times \frac{1}{ hc }\right]=\frac{ Fr ^{2}}{ E \lambda}=\left( M ^{0} L ^{0} T ^{0}\right)\)
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