Question

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

• A. $[M^{0} L^{0} T^{-1}]$
• B. $[M^{0}L^{-1} T^{-1}]$
• C. $[M^{2}LT^{-3}]$
• D. $[M^{0}L^{-1}T^{0}]$

Answer 1

Answer: (D)

In Bohr’s model, $\frac{1}{\lambda}=\frac{me^{4}}{\varepsilon_{0}^{2}h^{3}c} \left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$
where $\lambda$= wavelength, $n_{1}$ and $n_{2}$ are principal quantum numbers.
$\therefore \left[\frac{me^{4}}{\varepsilon_{0}^{2}h^{3}c}\right]= \left[L^{-1}\right]=\left[M^{0}L^{-1}T^{0}\right]$