Question

The dimension of the quantity $\frac{1}{\varepsilon_{0}} \frac{e^{2}}{h c}$ is $(e=$ charge of electron, $h=$ Planck's constant and $c=$ velocity of light)

• A. $\left[ M ^{-1} L ^{-3} T ^{2} A \right]$
• B. $\left[ M ^{0} L ^{0} T ^{0} A ^{0}\right]$
• C. $\left[ ML ^{3} T ^{-4} A ^{-2}\right]$
• D. $\left[ M ^{-1} L ^{-3} T ^{4} A ^{2}\right]$

Answer 1

Answer: (B)

[Energy] $=\left[\frac{h c}{\lambda}\right]$
or $[h c]=[$ Energy $][\lambda]=[$ Force $][\text { Distance }]^{2}$
Also, [Force] $=\frac{\left[e^{2}\right]}{\left[\varepsilon_{0}\right][\text { Distance }]^{2}}$
or $\frac{\left[e^{2}\right]}{\left[\varepsilon_{0}\right]}=[$ Force $][\text { Distance }]^{2}$
$\therefore [h c]=\frac{\left[e^{2}\right]}{\left[\varepsilon_{0}\right]}$
or $\left[\frac{e^{2}}{\varepsilon_{0}} \cdot \frac{1}{h c}\right]$
$=\left[ M ^{0} L ^{0} T ^{0} A ^{0}\right]$