Why does velocity of electron increases with increase atomic number in the Bohr model of the hydrogen and hydrogen like atoms?

Emilio Calhoun

Emilio Calhoun

Answered question

2022-10-15

Why does velocity of electron increases with increase atomic number in the Bohr model of the hydrogen and hydrogen like atoms?

Answer & Explanation

Cavalascamq

Cavalascamq

Beginner2022-10-16Added 21 answers

The same reason the Earth would move faster should the mass of the sun increase: centripetal force grows. In the case of Bohr's model, the force grows as Z,
F e = k Z e 2 r 2
Newton's law thus results in
m v 2 r = F e = k Z e 2 r 2
leading to v Z 1 / 2
Evelyn Freeman

Evelyn Freeman

Beginner2022-10-17Added 5 answers

The total energy if the energy of the electron in the Bohr atom must be constant, since no agent is doing work on the electron. As the electron moves farther away from the nucleus, the potential energy of the electron decreases [ the electrostatic potential between the nucleus and the electron decreases with distance]. The kinetic energy has to increase, to keep the total energy constant. This directly implies an increase in velocity.

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