Calculate the ionization energy (eV) for a 'hydrogen-like' atom with one electron and Z = 4 from the excited state of n=2.

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
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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 \( n \).
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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