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An electron makes a transition from orbit n = 2 to orbit n = 1, in Bohr’s model of hydrogen atom. Consider change in mag…

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An electron makes a transition from orbit n = 2 to orbit n = 1, in Bohr’s model of hydrogen atom. Consider change in magnitudes of its kinetic energy (K) and potential energy (U).

a

K increases and U decreases

b

K decreases and U increases

c

Both K and U decrease

d

Both K and U increase

✓ Correct answer: a)

K increases and U decreases

Explanation

In Bohr's model of the hydrogen atom, the kinetic energy (\(K\)) and potential energy (\(U\)) of an electron in an orbit are related to its distance from the nucleus. When an electron transitions from a higher energy level (\(n=2\)) to a lower energy level (\(n=1\)), it loses energy. The kinetic energy of the electron is given by the formula \(K = \frac{1}{2}mv^2\), and the potential energy is given by \(U = -\frac{ke^2}{r}\), where \(r\) is the radius of the orbit. As the electron moves to a lower orbit (\(n=1\)), the radius decreases, leading to an increase in kinetic energy (since the electron moves faster in lower orbits) and a decrease in potential energy (since it is closer to the nucleus). Therefore, \(K\) increases and \(U\) decreases.
Identify the initial and final orbits: initial orbit \(n=2\), final orbit \(n=1\).

Understand that as the electron moves to a lower orbit, it loses energy.

Determine that kinetic energy increases because the electron moves faster in the lower orbit.

Determine that potential energy decreases because the electron is closer to the nucleus

A. \(K\) increases and \(U\) decreases

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