If m, e, ε0, h and c denote mass electron, charge of electron. Planckâs constant and speed of light, respectively. The dimensions of (me4/ε20 h3c)are

Question

If m, e, ε0, h and c denote mass electron, charge of electron. Planckâs constant and speed of light, respectively. The dimensions of (me4/ε20 h3c)are (A) [M0 L0 T-1] (B) [M0L-1 T-1] (C) [M2LT-3] (D) [M0L-1T0]

Tardigrade Admin · Accepted Answer

In Bohrâs model, (1/λ)=(me4/ε02h3c) ((1/n12)-(1/n22)) where λ= wavelength, n1 and n2 are principal quantum numbers. ∴ [(me4/ε02h3c)]= [L-1]=[M0L-1T0]

Q. 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

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

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

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

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

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 $n_{2}$ are principal quantum numbers.
$∴ [\frac{m e ^{4}}{ε _{0}^{2} h ^{3} c}] = [L^{- 1}] = [M^{0} L^{- 1} T^{0}]$

Q. If m, e, ε0​, h and c denote mass electron, charge of electron. Planck’s constant and speed of light, respectively. The dimensions of ε02​h3cme4​are

[M0L0T−1]

[M0L−1T−1]

[M2LT−3]

[M0L−1T0]