Certainly! Here's the transcribed content suitable for an educational website:---**Problem Statement:**Consider an electron orbiting around a proton with an orbital radius of \( R = 4.77 \times 10^{-10} \, \text{m} \). What is the orbital frequency of the electron motion? Use \( m_e = 9.11 \times 10^{-31} \, \text{kg} \), \( e = 1.6 \times 10^{-19} \, \text{C} \), and \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).**Questions:**1. The frequency, \( f_0 = \) [Input Field] Units [Dropdown Menu for Unit Selection].2. By how much would this frequency increase (assume the same orbital radius) if an external magnetic field of \( B = 0.5 \, \text{T} \) is applied to the system along the electron axis of rotation? The increase in the frequency, \( \Delta f = \) [Input Field] Units [Dropdown Menu for Unit Selection].---Ensure to fill in the calculations where required, and select the appropriate units from the dropdown menus provided.

The electrostatic force will act as centripetal force and can be equated to give velocity and frequency of revolution . however when magnetic field will be applied then force on electron will be radially inward and total centripetal force will increase and hence velocity of revolution will increase and frequency too. see the attached solution image

Answered: Consider an electron o orbital…

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Consider an electron o orbital frequency of the k = 9 x 10° Nm²/c² The frequency, fo -

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Chapter1: Units, Trigonometry. And Vectors

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Certainly! Here's the transcribed content suitable for an educational website:

---

**Problem Statement:**

Consider an electron orbiting around a proton with an orbital radius of \( R = 4.77 \times 10^{-10} \, \text{m} \). What is the orbital frequency of the electron motion? Use \( m_e = 9.11 \times 10^{-31} \, \text{kg} \), \( e = 1.6 \times 10^{-19} \, \text{C} \), and \( k = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 \).

**Questions:**

1. The frequency, \( f_0 = \) [Input Field] Units [Dropdown Menu for Unit Selection].

2. By how much would this frequency increase (assume the same orbital radius) if an external magnetic field of \( B = 0.5 \, \text{T} \) is applied to the system along the electron axis of rotation?

The increase in the frequency, \( \Delta f = \) [Input Field] Units [Dropdown Menu for Unit Selection].

---

Ensure to fill in the calculations where required, and select the appropriate units from the dropdown menus provided.

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