How fast is the electron moving in the first Bohr orbit? A) 3.3 × 10⁶ m/s B) 2.2 × 10⁶ m/s C) 4.4 × 10⁶ m/s D) 5.5 × 10⁶ m/s E) 5.5 × 10¹⁵ m/s

Question

Quizplus · Accepted Answer

The speed of electron in the first Bohr orbit can be calculated by using the formula v = (Z/n) * (e^2/4πε0m), where Z is the atomic number, n is the principal quantum number, e is the elementary charge, ε0 is the permittivity of free space and m is the mass of the electron. For hydrogen atom, Z = 1 and n = 1. Substituting the values, we get v = (1/1) * (ke^2/me^2) = (ke^2/me^2) = (9×10^9) * (1.6×10^-19)^2 / (9.1×10^-31) = 2.2 × 10^6 m/s (approximately). Therefore, the correct choice is B.

How Fast Is the Electron Moving in the First Bohr