Consider the following statements about the Bohr model of a hydrogen-like ion. (I) In any stationary orbit the kinetic energy equals the magnitude of the total energy. (II) In any stationary orbit the

Question

Consider the following statements about the Bohr model of a hydrogen-like ion.

(I) In any stationary orbit the kinetic energy equals the magnitude of the total energy.

(II) In any stationary orbit the potential energy is twice the total energy.

(III) The frequency of revolution of the electron is proportional to $Z^{2} / n^{3}$ .

(IV) The energy gap between successive levels increases as n increases.

Which of the statements are correct?

TestHub · Accepted Answer

KE = -E, so (I) is true. PE = 2E, so (II) is true.

Frequency = $v / (2 π r)$ , which is proportional to $(Z / n) / (n^{2} / Z) = Z^{2} / n^{3}$ : (III) is true.

$E_{n + 1} - E_{n}$ decreases as n rises: (IV) is false.

Answer: (B).

Chemistry - Atomic Structure Question with Solution | TestHub