Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![**Ionization Energy Calculation for a Hydrogen-like Atom**
This interactive tool assists in calculating the ionization energy (in electron volts, eV) for a 'hydrogen-like' atom which consists of a single electron. The task is to determine the energy required to ionize an atom with an atomic number \( Z = 4 \) from an excited state where the principal quantum number \( n = 2 \).
### Instructions:
1. **Input Area**: Enter the calculated ionization energy in the field labeled "eV."
2. **Keypad**: Use the keypad below to input your answer. It includes numbers 0-9 and special functions:
- **Backspace (←)**: To delete the last entered digit.
- **C**: To clear all input.
- **+/−**: To toggle the sign of the number.
- **Decimal (.)**: To insert a decimal point.
- **Exponential (x 10ᵦ)**: To enter numbers in scientific notation.
### Concept Overview:
In a hydrogen-like ion, with only one electron, the ionization energy can be calculated using the formula derived from the Bohr model of the atom:
\[ E = 13.6 \, \text{eV} \times \frac{Z^2}{n^2} \]
Where:
- \( E \) is the ionization energy in electron volts (eV),
- \( Z \) is the atomic number (4 in this case),
- \( n \) is the principal quantum number of the electron's current energy level (2 for this calculation).
Use this tool to explore and understand how ionization energy changes with different values of \( Z \) and \( n \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4f6f55f-74e4-4811-89c3-6145bf7c8bd8%2F6501bf15-7d3d-4a95-9cf4-63e37dcc1a67%2Fdh6o6c_processed.png&w=3840&q=75)
Transcribed Image Text:**Ionization Energy Calculation for a Hydrogen-like Atom**
This interactive tool assists in calculating the ionization energy (in electron volts, eV) for a 'hydrogen-like' atom which consists of a single electron. The task is to determine the energy required to ionize an atom with an atomic number \( Z = 4 \) from an excited state where the principal quantum number \( n = 2 \).
### Instructions:
1. **Input Area**: Enter the calculated ionization energy in the field labeled "eV."
2. **Keypad**: Use the keypad below to input your answer. It includes numbers 0-9 and special functions:
- **Backspace (←)**: To delete the last entered digit.
- **C**: To clear all input.
- **+/−**: To toggle the sign of the number.
- **Decimal (.)**: To insert a decimal point.
- **Exponential (x 10ᵦ)**: To enter numbers in scientific notation.
### Concept Overview:
In a hydrogen-like ion, with only one electron, the ionization energy can be calculated using the formula derived from the Bohr model of the atom:
\[ E = 13.6 \, \text{eV} \times \frac{Z^2}{n^2} \]
Where:
- \( E \) is the ionization energy in electron volts (eV),
- \( Z \) is the atomic number (4 in this case),
- \( n \) is the principal quantum number of the electron's current energy level (2 for this calculation).
Use this tool to explore and understand how ionization energy changes with different values of \( Z \) and \( n \).
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