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Q.

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

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a

$[M^{0} {LT}^{- 1}]$

b

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

c

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

d

$[M^{2} {LT}^{- 3}]$

answer is D.

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Detailed Solution

In Bohr's model, $\frac{1}{λ} = \frac{{me}^{4}}{{ε_{0}}^{2} h^{3} c} (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}})$

where $λ = wavelength, n_{1} and n_{2} are principal quantum numbers .$

$∴ [\frac{{me}^{4}}{{ε_{0}}^{2} h^{3} c}] = [L^{- 1}] = [M^{0} L^{- 1} T^{0}]$

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