In the planetary model of the hydrogen atom, it is assumed that the electron moves around the proton

| May 8, 2021 | education

In the planetary model of the hydrogen atom, it is assumed that the electron moves around the proton with an angular velocity of 10 ^ 16 rad / s. Find the radius of the orbit.

To calculate the radius of the orbit of the electron under consideration, we use the equality: me * ac = F = k * qe * qp / r ^ 2; me * ω ^ 2 * r = F = k * qe ^ 2 / r ^ 2, whence we express: r = (k * qe ^ 2 / (me * ω ^ 2)).

Data: k – coefficient of proportionality (k = 9 * 10 ^ 9 m / F); qe – electron charge (qe = -1.6 * 10 ^ -19 C); me is the mass of an electron (me = 9.11 * 10 ^ -31 kg); ω is the angular velocity of the electron under consideration (ω = 10 ^ 16 rad / s).

Calculation: r = (k * qe2 / (me * ω2)) ^ 1/3 = (9 * 10 ^ 9 * (1.6 * 10 ^ -19) ^ 2 / ((9.11 * 10 ^ -31 ) * (1016) ^ 2)) ^ 1/3 = 1.36 * 10 ^ -10 m.

Answer: The radius of the orbit of the electron in question is 1.36 * 10 ^ -10 m.



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