In a simple model of the Hydrogen atom, an electron moves in uniform circular motion with a speed of 2.2 x 106 m/s around a proton. (a) Determine the radius of the electron’s orbit. (b) Find the centripetal acceleration of the electron in this orbit.

a) Radius of electron' s orbit = 5.29 × 10⁻¹¹ m

b) Centripetal Acceleration, α = 9.15 × 10²² m/s²

Explanation:

The force of attraction between a proton and an electron of the simple model of Hydrogen atom is obtained from literature to be 8.325 × 10⁻⁸ N

It is this force that is driving the the circular motion of the electron. Centripetal force is given by

F = mv²/r

r = mv²/F

m = mass of the electron = 9.11 × 10⁻³¹ kg

v = velocity of the electron = 2.2 × 10⁶ m/s

r = 9.11 × 10⁻³¹ × (2.2 × 10⁶)²/(8.325 × 10⁻⁸)

r = 5.29 × 10⁻¹¹ m

b) centripetal acceleration, α = F/m or v²/r

α = (8.325 × 10⁻⁸)/(9.11 × 10⁻³¹) = (2.2 × 10⁶)²/(5.29 × 10⁻¹¹) = 9.15 × 10²² m/s²

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