The Radius of Electron Orbit within a Hydrogen Atom
Calculation of the Radius of Electron Orbit within a Hydrogen Atom
A hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary, and the electron has a speed of 7.8 x 10^5 m/s. We need to find the radius between the stationary proton and the electron orbit within the hydrogen atom.
Formula and Calculation
To answer this, we need to simplify and rearrange the formula for force in circular motion:
F = mv^2/r = k(q1q2)/r^2
Rearranged for the radius (r), we get:
r = (k*q1q2)/(mv^2)
Plugging in the values:
r = (9 x 10^9) x ((1.5 x 10^-19)^2) / (9 x 10^-31) x ((7.8 x 10^5)^2)
Result
After calculation, the radius of the electron orbit within the hydrogen atom is approximately 4.161 x 10^-10 meters. Therefore, the distance between the stationary proton and the electron orbit is 4.161 Å (angstroms).
A hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary, and the electron has a speed of 7.8 x 10^5 m/s. Find the radius between the stationary proton and the electron orbit within the hydrogen atom.
To answer this, one must simplify and rearrange the formula for force in a circular motion: (me(v^2)/r) = (k9^2/r^x). Rearranged for Radius is: r = (k9^2)/(me(v^2)). Based on the conditions this gives you: r = (9*(10^9)x*((1.5*10^-19)^2)) / (9*(1*10^-31)*((7.8*(10^5))^2)). This will give you 4.161 x (10^-10) = 4.161 Å