Question

The quantity $\frac{e^2}{2h{\epsilon }_{0}c}$ has a value

• A. $\frac{1}{137}m{s}^{-1}$
• B. $\frac{2}{137}m{s}^{-1}$
• C. $\frac{1}{137}$
• D. $\frac{2}{137}$

Answer 1

Answer: (C)

$\frac{1}{137}$

$\frac{e^2}{2h{\epsilon }_{0}c}=\frac{(1.6\times {10}^{-19}{)}^2}{2\times 6.26\times {10}^{-34}\times 8.857\times {10}^{-12}\times 3\times {10}^8}$

$=\frac{1}{137}$ it is unit less quality

Substitute the values of all constants. (standard) with appropriate units
$e=1.6\times {10}^{-19}C$
$h=6.26\times {10}^{-34}$
${ϵ}_o=8.857\times {10}^{-12}$
$c=3\times {10}^{8}m/s$