What is the Energy of an Electron in a Bohr Orbit?

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Grade Level:

Class 12

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Definition

What is it?

The energy of an electron in a Bohr orbit refers to the total energy an electron possesses when it revolves around the nucleus in a specific, stable path. This energy is a combination of its kinetic energy (due to motion) and potential energy (due to attraction to the nucleus). For each orbit, the electron has a fixed, quantized energy value.

Simple Example

Quick Example

Imagine you are climbing stairs in your school building. Each step you stand on has a fixed height from the ground. You can't float between steps; you are either on one step or the next. Similarly, an electron in a Bohr atom can only have specific, fixed energy levels, like standing on a particular stair step, and not any energy in between.

Worked Example

Step-by-Step

Let's calculate the energy of an electron in the first Bohr orbit (n=1) for a hydrogen atom (Z=1).

Step 1: Recall the formula for the energy of an electron in the nth Bohr orbit: En = -13.6 * (Z^2 / n^2) eV. Here, eV stands for electron volt, a unit of energy.
---Step 2: Identify the given values. For a hydrogen atom, Z (atomic number) = 1. For the first orbit, n (principal quantum number) = 1.
---Step 3: Substitute these values into the formula: E1 = -13.6 * (1^2 / 1^2) eV.
---Step 4: Calculate the result: E1 = -13.6 * (1 / 1) eV.
---Step 5: E1 = -13.6 eV.
---Answer: The energy of an electron in the first Bohr orbit of a hydrogen atom is -13.6 electron volts.

Why It Matters

Understanding electron energy levels is crucial for designing new materials in Engineering, as it dictates how atoms interact. In Medicine, it helps develop diagnostic tools like MRI. It's also fundamental for developing advanced sensors in Space Technology and understanding reactions in Biotechnology, shaping our future careers.

Common Mistakes

MISTAKE: Forgetting the negative sign in the energy formula, which indicates the electron is bound to the nucleus. | CORRECTION: Always include the negative sign. It shows that energy must be supplied to remove the electron from the atom.

MISTAKE: Confusing 'n' (principal quantum number) with 'Z' (atomic number) in the formula. | CORRECTION: 'n' represents the orbit number (1, 2, 3...), while 'Z' represents the number of protons in the nucleus (e.g., 1 for hydrogen, 2 for helium).

MISTAKE: Not squaring 'Z' and 'n' correctly in the formula, or squaring only one of them. | CORRECTION: Remember the formula is Z^2 divided by n^2. Both terms must be squared before division.

Practice Questions

Try It Yourself

QUESTION: What is the energy of an electron in the second Bohr orbit (n=2) of a hydrogen atom (Z=1)? | ANSWER: -3.4 eV

QUESTION: An electron in a certain Bohr orbit of a hydrogen-like atom has an energy of -6.04 eV. If the atomic number (Z) is 2 (Helium ion), what is the principal quantum number (n) of this orbit? | ANSWER: n = 2

QUESTION: Calculate the ratio of the energy of an electron in the first Bohr orbit of a hydrogen atom to the energy of an electron in the second Bohr orbit of a Helium ion (Z=2). | ANSWER: Ratio = 4:1 (or 4)

MCQ

Quick Quiz

Which of the following statements about the energy of an electron in a Bohr orbit is TRUE?

The energy is always positive.

The energy is quantized, meaning it can only have specific discrete values.

The energy increases as the electron gets closer to the nucleus.

The energy depends only on the atomic number, not the orbit number.

The Correct Answer Is:

Bohr's model states that electrons occupy fixed orbits, each with a specific, quantized energy level. The negative sign indicates the electron is bound, and energy decreases (becomes more negative) closer to the nucleus.

Real World Connection

In the Real World

This concept helps us understand why different elements produce unique colours when heated, like the vibrant colours in fireworks during Diwali or a wedding celebration. The specific energy levels determine which colours of light atoms can absorb and emit, a principle used in LED lights and spectrophotometers in labs.

Key Vocabulary

Key Terms

BOHR ORBIT: A fixed, circular path an electron takes around the nucleus. | QUANTIZED ENERGY: Energy that can only exist in discrete, specific amounts, not continuous values. | ATOMIC NUMBER (Z): The number of protons in an atom's nucleus. | PRINCIPAL QUANTUM NUMBER (n): A number (1, 2, 3...) that describes the energy level or shell of an electron. | ELECTRON VOLT (eV): A unit of energy commonly used in atomic and nuclear physics.

What's Next

What to Learn Next

Great job understanding electron energy! Next, explore 'Bohr's Model of the Atom' in more detail. This will help you see how these energy levels are derived from the model's postulates and connect it to atomic spectra.