First slide

Dimensions of physical quantities

Question

If m, e, $ε_{0}$ , h and c denote mass electron, charge of electron. Planck's constant and speed of light, respectively. The dimensions of $\frac{m e^{4}}{ε_{0}^{2} h^{3} c}$ are

Moderate

A

$[M^{0} L^{0} T^{- 1}]$
B

$[M^{0} L^{- 1} T^{- 1}]$
C

$[M^{2} L T^{- 3}]$
D

$[M^{0} L^{- 1} T^{0}]$

Solution

$In Bohr's model, \frac{1}{λ} = \frac{m e^{4}}{ε_{0}^{2} h^{3} c} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$
where $λ = wavelength, n_{1} and n_{2}$ principal quantum numbers.
$∴ [\frac{m e^{4}}{ε_{0}^{2} h^{3} c}] = [L^{- 1}] = [M^{0} L^{- 1} T^{0}]$

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