The radius of the first Bohr orbit for hydrogen atom is: 

CONCEPT:

Bohr's Model of the Atom

• According to Bohr's model, the electron in a hydrogen atom moves in a circular orbit around the nucleus under the influence of the Coulomb force.
• The radius of the electron's orbit is quantized and is given by the formula:

  r_n = n² × a₀

• Here:
  • r_n is the radius of the nth orbit.
  • n is the principal quantum number (n = 1 for the first orbit).
  • a₀ is the Bohr radius, which is a constant with a value of approximately 0.529 × 10^-10 meters or 0.53 × 10^-8 cm.

EXPLANATION:

• The first Bohr orbit corresponds to n = 1.
• The radius of the first Bohr orbit (r₁) is therefore:

  r₁ = 1² × a₀ = a₀

• Substituting the value of a₀, we get:

  r₁ = 0.53 × 10^-8 cm

Therefore, the radius of the first Bohr orbit for the hydrogen atom is 0.53 × 10^-8 cm.