Calculate the electron rotation frequency using Bohr's theory

Let's calculate the frequency of rotation of an electron in a hydrogen atom at the second energy level according to Bohr's theory.

Given: the electron is in the second energy level.

Required to find: electron rotation frequency.

Answer:

According to Bohr's theory, the radius of the nth energy level of the hydrogen atom can be calculated using the formula:

r_n = n^2 * a_0,

where a_0 is Bohr's constant equal to 0.529 * 10^-10 m.

Radius of the second energy level:

r_2 = 2^2 * a_0 = 4 * 0.529 * 10^-10 m = 2.12 * 10^-10 m.

Electron speed at the second energy level:

v_2 = (Ze^2 / (4πε_0r_2m_e))^1/2,

where Z is the nuclear charge, e is the elementary charge, ε_0 is the electrical constant, m_e is the electron mass.

For a hydrogen atom Z = 1, m_e = 9.109 * 10^-31 kg.

Then the speed of the electron at the second energy level is:

v_2 = (1 * (1.602 * 10^-19)^2 / (4π * 8.854 * 10^-12 * 2.12 * 10^-10 * 9.109 * 10^-31))^1/2 ≈ 1, 97 * 10^6 m/s.

Electron rotation frequency at the second energy level:

f_2 = v_2 / (2πr_2) ≈ 6,56 * 10^15 Гц.

Answer: the rotation frequency of an electron at the second energy level of the hydrogen atom, according to Bohr's theory, is approximately 6.56 * 10^15 Hz.

Calculation of the electron rotation frequency according to Bohr's theory

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This product allows you to easily and quickly calculate the frequency of rotation of an electron in a hydrogen atom at the second energy level according to Bohr's theory. To do this, you need to know that the radius of the second energy level of the hydrogen atom can be calculated using the formula r_2 = 2^2 * a_0, where a_0 is Bohr's constant, equal to 0.529 * 10^-10 m. The speed of the electron at the second energy level can be calculated using the formula v_2 = (Ze^2 / (

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This product is a detailed solution to problem 60344 in physics, in which it is necessary to calculate the rotation frequency of the electron of a hydrogen atom at the second energy level in accordance with Bohr's theory. The product description contains a brief record of the conditions of the problem, formulas and laws used in the solution, the derivation of the calculation formula and the answer to the problem. If the buyer has any questions about the solution, the author of the product is ready to help.

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