Final answer:
The ratio of the speed of an electron in the first Bohr orbit of hydrogen to the speed of light is e²/(2πh), where e is the elementary charge, π is Pi, and h is Planck's constant. The correct answer is option c.
Step-by-step explanation:
The question is concerned with finding the ratio of the speed of an electron in the first Bohr orbit of hydrogen to the speed of light. In the Bohr model of the hydrogen atom, the speed v of an electron in the first orbit (n=1) can be calculated using the formula v = e²/(2ε₀h), where e is the elementary charge, ε₀ is the permittivity of free space, and h is Planck's constant.
The speed of light c is a well-known physical constant. Therefore, the ratio of their speeds is v/c = e²/(2ε₀hc). Substituting the values in SI units and converting to cgs units, where the permittivity of free space ε₀ is replaced by 1/(4πc) in cgs units, produces the ratio as e²/(2hε₀c) = e²/(2πh).