If an electron is moving around a nucleus of charge 2 e in a...

If an electron is moving around a nucleus of charge $2 e$ in a circular orbit of radius $10^{-10} \mathrm{~m}$, then the initial frequency of light emitted by the electron is: (a) $4.2 \times 10^{15} \mathrm{~Hz}$ (b) $0.36 \times 10^{15} \mathrm{~Hz}$ (c) $3.6 \times 10^{15} \mathrm{~Hz}$ (d) $4.2 \times 10^{15} \mathrm{~Hz}$

If an electron is moving around a nucleus of charge $2 e$ in a circular orbit of radius $10^{-10} \mathrm{~m}$, then the initial frequency of light emitted by the electron is:
(a) $4.2 \times 10^{15} \mathrm{~Hz}$
(b) $0.36 \times 10^{15} \mathrm{~Hz}$
(c) $3.6 \times 10^{15} \mathrm{~Hz}$
(d) $4.2 \times 10^{15} \mathrm{~Hz}$

Key Concepts

Bohr Model

The Bohr model explains the quantized nature of electron orbits in atoms. It postulates that electrons orbit the nucleus in discrete circular orbits without radiating energy, and that the angular momentum is quantized. Transitions between these orbits result in the emission or absorption of photons with an energy equal to the difference between the initial and final energy levels, as described by E = h×?, where h is Planck's constant and ? is the frequency of light.

Coulomb Force and Centripetal Motion

In an atom, the negatively charged electron is held in orbit around the positively charged nucleus by the Coulomb force of attraction. For a stable circular orbit, the inward Coulomb (electrostatic) force must balance the electron's required centripetal force. This balance is used to determine quantities such as the electron’s orbital speed, and from there parameters like the orbital (or revolution) frequency can be computed.

Radiation Frequency and Energy Transitions

When an electron transitions between energy levels, the energy difference is released or absorbed in the form of a photon. The frequency of the photon is determined by dividing the energy difference by Planck's constant (? = ?E/h). In problems involving electrons in atoms, knowing the orbital parameters and using the energy quantization conditions allows one to calculate the characteristic frequency of the light emitted during such transitions.

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