Problem 26 - Chemistry in 30 days

Question

Energy of Bohr's orbit: (a) increases as we move away from the nucleus (b) decreases as we move away from the nucleus (c) remains the same as we move away from the nucleus (d) none of these

Step-by-Step Solution

Answer

(a) increases as we move away from the nucleus.

Step 1: Understand Bohr's Model

Bohr's model describes electrons orbiting the nucleus in specific orbits or energy levels. These orbits are assigned quantum numbers (n=1,2,3,...), with n=1 being the closest to the nucleus.

Step 2: Bohr's Energy Formula

The energy of an electron in a specific orbit according to Bohr's model is given by the formula: \( E_n = -\frac{13.6\text{ eV}}{n^2} \) where \( n \) is the principal quantum number, and energy is measured in electron volts (eV).

Step 3: Evaluate Energy Change

According to the formula, as \( n \) increases, the denominator \( n^2 \) increases, making the fraction smaller and therefore making the energy \( E_n \) less negative. So, \( E_n \) increases (becomes less negative) as \( n \) increases.

Step 4: Select the Correct Option

Since \( E_n \) increases (becomes less negative) as we move away from the nucleus (higher \( n \) values), option (a) is correct, which states that energy increases as we move away from the nucleus.

Key Concepts

Energy Levels

In Bohr's Model, energy levels are specific, quantized orbits around the nucleus where electrons can reside. These levels are crucial because they dictate how an electron behaves around a nucleus. One important thing to remember about energy levels is that they are not continuous; electrons cannot exist at energy levels that don't fit the Bohr model's conditions. Understanding how electrons occupy these distinct orbits is fundamental in quantum mechanics.
The principal quantum number \( n \) is what helps distinguish between these various energy levels:

• **\( n = 1\)** is the closest orbit to the nucleus and is known as the ground state.
• As \( n\) increases, energy levels become further from the nucleus, and electrons require more energy to transition between these orbits.
• Each increase in \( n \) also signifies the move to a higher potential energy because the attraction between the electron and the nucleus weakens.

Quantum Numbers

Quantum numbers are essentially the addresses for electrons within an atom. They provide detailed information about an electron's position and motion in an atom. In the Bohr model, the primary quantum number, denoted by \( n\), tells us the electron's energy level or shell.
Here's how quantum numbers come into play:

• **Principal Quantum Number \( n \)**: Determines the size and energy level of the orbital. The larger the value of \( n\), the farther the electron is from the nucleus.
• It's important to remember that these are whole numbers starting from 1 and moving onwards (1, 2, 3, ...).
• These numbers help pinpoint which energy level the electron is in and how much energy is associated with that particular level.

Electron Volts (eV)

Electron volts (eV) play a pivotal role in describing the energy values in atomic and particle physics. It is a small unit of energy used largely for atomic-scale physics, especially concerning electrons. Simply put, one electron volt is the amount of kinetic energy gained or lost by an electron when it is accelerated through a potential difference of one volt.
Why is using eV practical?

• Since the energies of electrons in atoms are comparatively small, using eV provides a more manageable number rather than joules, the standard SI unit of energy.
• This unit helps avoid dealing with unwieldy decimal places and makes calculations as well as comparisons more intuitive.
• For instance, in Bohr's Model, the energy of an electron in a shell is expressed using eV, such as the energy value -13.6 eV for the first electron shell (\( n = 1 \)).