Question

Estimate the orbital velocity in m/s of an electron orbiting the nucleus of a hydrogen atom at a
radius of 0.05 nm.

Answer 1

Answer on Question #43091-Physics-Atomic Physics

Estimate the orbital velocity in m/s of an electron orbiting the nucleus of a hydrogen atom at a radius of 0.05 nm.

SOLUTION:

The centripetal force which keeps the electron in orbit is provided by the electric force.

$$\frac {m v ^ {2}}{r} = \frac {k e ^ {2}}{r ^ {2}}$$

So,

$$v = \sqrt {\frac {k}{m r}} e = \sqrt {\frac {9 \cdot 1 0 ^ {9} \frac {N m ^ {2}}{C ^ {2}}}{9 . 1 1 \cdot 1 0 ^ {- 3 1} k g \cdot 0 . 0 5 \cdot 1 0 ^ {- 9} m}} \cdot 1. 6 \cdot 1 0 ^ {- 1 9} C = 1. 4 \cdot 1 0 ^ {6} \frac {m}{s}.$$

Answer: $1.4 \cdot 10^{6} \frac{m}{s}$ .

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