According to Bohr's model of the hydrogen atom, the radius of the first orbit (also known as the ground state) can be calculated using the following equation:
r = (n^2 * h^2 * ε₀) / (π * m * e^2)
Where:
- r is the radius of the orbit
- n is the principal quantum number (in this case, n = 1 for the ground state)
- h is Planck's constant (6.626 x 10^-34 J s)
- ε₀ is the permittivity of free space (8.85 x 10^-12 F/m)
- m is the mass of the electron (9.11 x 10^-31 kg)
- e is the elementary charge (1.60 x 10^-19 C)
Using these values in the equation gives:
r = (1^2 * (6.626 x 10^-34 J s)^2 * 8.85 x 10^-12 F/m) / (π * 9.11 x 10^-31 kg * (1.60 x 10^-19 C)^2)
Simplifying this expression yields a radius of approximately 5.29 x 10^-11 meters, which is known as the Bohr radius.