Question

Verify the equation ( rₙ = n² ZaB ) using the approach stated in the . Equate the Coulomb and centripetal forces, and insert an expression for velocity from the condition for angular momentum quantization.

a) ( rₙ = n² ZaB )
b) ( aB = {h²}/{4π²mₑk²e²} = 0.529 × 10¹⁰ , {m} )
c) Both a and b
d) None of the above

Answer 1

a) ( rₙ = n² ZaB )

To verify the equation (rₙ = n² ZaB), the approach stated in the text is to equate the Coulomb and centripetal forces and insert an expression for velocity from the condition for angular momentum quantization.

Step-by-step explanation:

In order to verify the equation (rₙ = n² ZaB) using the approach stated in the text, we need to equate the Coulomb and centripetal forces and then insert an expression for velocity from the condition for angular momentum quantization.

First, we equate the Coulomb force and the centripetal force to get the expression (4π²mₑk²e⁴/rₙ³) = (mₑv²/rₙ). Rearranging this equation, we get (v² = (4π²mₑk²e⁴)/rₙ⁴).

Next, we substitute this expression for velocity into the equation for angular momentum quantization (mₑvrₙ = nh/2π). Solving for rₙ, we obtain (rₙ = n² ZaB).