(455) HL Bohr model for hydrogen [IB Physics HL]

Bohr Model of the Atom

• The Bohr model describes the hydrogen atom with stable orbits for electrons.

• Key concepts include:

  • Electrons are in stable orbits without emitting radiation, unlike predictions by classical physics.

  • Electrons can transition between energy levels and emit or absorb photons.

Electron Orbits and Energy Levels

• Energy levels are quantized, meaning electrons can only exist in specific orbits based on quantum numbers:

  • The energy emitted when transitioning is given by E = hf.

• The angular momentum of electrons is quantized in integer amounts of ( \frac{h}{2\pi} ).

  • ( n ): an integer representing quantum number; valid values are positive integers (1, 2, 3, ...).

Key Equations and Constants

• Relevant parameters include:

  • Mass of the electron: ( 9.11 \times 10^{-31} ) kg

  • Planck's constant: ( h = 6.63 \times 10^{-34} ) Js

• Energy of the nth orbit: ( E_n = -\frac{3.6}{n^2} ) eV, applicable for hydrogen:

  • n = 1: ( -3.6 ) eV

  • n = 2: ( -\frac{13.6}{4} ) eV (4 eV)

Energy Transitions Example

• Consider an electron transitioning from n = 3 to n = 1:

  • Calculate the energy for each state:

    • ( E_3 = -\frac{3.6}{9} = -1.51 ) eV

    • ( E_1 = -3.6 ) eV

• Change in energy, ( \Delta E ): ( 1.51 - 3.6 = 12.09 ) eV.

Wavelength Calculation

• Convert energy to joules (1 eV = ( 1.6 \times 10^{-19} ) J):

  • ( \Delta E = 12.09 \times 1.6 \times 10^{-19} = 1.9 \times 10^{-18} ) J.

• Use the wave equation to find wavelength ( \lambda ):

  • ( \lambda = \frac{hc}{E} )

  • Result: ( \lambda \approx 1.0 \times 10^{-7} ) m (100 nm), in UV range (not visible).

Notes

• Understanding angular momentum, quantization, and energy transitions is critical for the IB syllabus.

• Be familiar with using provided equations and constants in calculations.