Question

What is the trend of energy of Bohr's orbits? (a) Energy of the orbit increases as we move away from the nucleus. (b) Energy of the orbit decreases as we move away from the nucleus. (c) Energy remains same as we move away from the nucleus. (d) Energy of Bohr's orbit cannot be calculated.

Short answer

The energy of Bohr's orbits increases as we move away from the nucleus.

Step-by-step solution

Understand the Bohr Model

Recognize that the Bohr model describes the atom with electrons orbiting the nucleus in specific energy levels or shells. Each shell has a quantized energy level, which means that the energy is fixed and distinct for each orbit.

Recall the Energy Formula for Bohr's Orbits

Remember that the energy associated with each orbit in the Bohr model is given by the formula \( E_n = -\frac{{R_H Z^2}}{{n^2}} \), where \( E_n \) is the energy of the nth orbit, \( R_H \) is the Rydberg constant for hydrogen, \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)), and \( n \) is the principal quantum number (orbit number).

Analyze the Trend in the Formula

From the formula, observe that as the principal quantum number \( n \) increases (which means we are moving away from the nucleus), the value of \( E_n \) becomes less negative, which implies that the energy of the orbit increases. Thus, energy levels become closer as \( n \) increases and converges to zero, which is the ionization energy of the electron.

Conclude the Correct Option

From Step 3, we conclude that as we move away from the nucleus to higher numbered orbits, the energy of the orbit increases. This matches option (a), therefore, option (a) is the correct answer.

Key concepts

Energy levels in atoms

Atoms are fundamental units of matter composed of a dense nucleus surrounded by electrons that orbit in discrete regions called energy levels or shells. An essential aspect of understanding atomic behavior is recognizing that these electrons do not exist just anywhere around the nucleus; they reside in specific energy levels.

Each energy level can be compared to the rungs of a ladder, where electrons can jump from one level to another but cannot exist between them. When an electron is in a lower energy level, it is closer to the nucleus and in a more bound state. As electrons absorb energy, they can move to higher energy levels, which are further away from the nucleus.

This aspect of atomic structure is vital for explaining why atoms only absorb and emit light at certain wavelengths and is a key element in the study of quantum mechanics.

Bohr's orbits energy trend

The Bohr Model, named after the physicist Niels Bohr, portrays the atom with a small, positively charged nucleus surrounded by electrons that travel in circular orbits. These orbits represent fixed energy levels, and a quantized energy level means that the value can only be certain amounts and nothing in between.

According to Bohr's model, the trend in the energy of these orbits is quite specific. As you move away from the nucleus, the principal quantum number, denoted by 'n', increases. The energy associated with these orbits follows the inverse square law relative to 'n'. As a result, the further away an electron is from the nucleus, the higher its potential energy becomes.

The energy trend in Bohr's orbits clarifies why higher orbits are less stable and more likely to allow the electron to escape, a phenomenon fundamental to understanding atomic emissions and the formation of ions.

Atomic structure

The atomic structure is the arrangement of subatomic particles within an atom. Central to this structure is the nucleus, which contains positively charged protons and neutral neutrons. Electrons, with negative charge, are found in energy levels around the nucleus.

The simplistic Bohr model is crucial in visualizing the atomic structure and explaining the electronic configuration of atoms, especially for light elements. However, modern atomic theory has moved beyond Bohr's model, incorporating the principles of quantum mechanics to provide a more accurate and complex picture of electron behavior, such as the probability of finding an electron in a certain region around the nucleus, known as an orbital.

Nevertheless, the atomic structure, as described by Bohr, provides an essential foundation for understanding chemical reactions, bonding, and the properties of matter at the atomic level.