Question

What is the Bohr radius (a_B) in meters, given the equation (a_B = frac{{hbar}}{{2π me²kq²}})?

a) (0.529 × 10⁻¹⁰m)
b) (1.097 × 10⁷m)
c) (2.34 × 10⁻¹¹m)
d) (4.678 × 10⁻¹⁰m)

Answer 1

The value of the Bohr radius (a_B) in meters, as given in the question, is 0.529 × 10⁻¹⁰ m which corresponds to option a).

Step-by-step explanation:

The Bohr radius (aB) is an important physical constant in quantum mechanics, particularly in the Bohr model of the atom. You've asked for the value of the Bohr radius in meters, which is given by the equation:

aB = í▮ä™∞á

After substituting the relevant physical constants into the equation, the Bohr radius can be found to be 0.529 × 10⁻¹⁰ m. This value corresponds to choice a), which is the correct answer and measures the average distance between the proton and the electron in the hydrogen atom in its ground state.

The Bohr radius provides a scale for describing the size of hydrogen-like atoms and ionized systems where one electron orbits around a single nucleus.