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Based on equation E = -2.178 xx 10^-18 J...

Based on equation `E = -2.178 xx 10^-18 J((Z^2)/(n^2))`, certain conclusions are written. Which of them is not correct ?

A

The negative sign in equation simply means that the energy of electron bound to the nucleus is lower than it would be if the electrons were at the infinite distance from the nucleus.

B

Larger the value of n, the larger is the orbit radius.

C

Equation can be used to calculate the change in energy when the electron changes orbit.

D

For n = 1, the electron has a more negative energy that it does for n = 6 which means that the electron is more loosely bound in the smallest allowed orbit.

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The correct Answer is:
To determine which conclusion based on the equation \( E = -2.178 \times 10^{-18} \, \text{J} \left( \frac{Z^2}{n^2} \right) \) is not correct, we will analyze each statement one by one. ### Step-by-Step Solution: 1. **Understanding the Equation**: - The equation represents the energy of an electron in a hydrogen-like atom, where \( Z \) is the atomic number and \( n \) is the principal quantum number (energy level). - The negative sign indicates that the energy is lower (more negative) when the electron is bound to the nucleus compared to when it is free (at infinity). 2. **Analyzing the Statements**: - **Statement 1**: The negative sign in this equation means that the energy of the electron bound to the nucleus is lower compared to the electron at infinite distance. - **Analysis**: This statement is true. A bound electron has lower energy than a free electron. - **Statement 2**: Larger the value of \( n \), larger is the orbit radius. - **Analysis**: This statement is also true. According to Bohr's model, the radius of the orbit increases with increasing \( n \). - **Statement 3**: This equation can be used to calculate the change in energy when the electron changes the orbit. - **Analysis**: This statement is true. The equation can be used to find the energy difference when an electron transitions between energy levels. - **Statement 4**: For \( n = 1 \), the electron has more negative energy than it does for \( n = 6 \), indicating that the electron is loosely bound in the smallest allowed orbit. - **Analysis**: This statement is incorrect. An electron in the \( n = 1 \) shell is more tightly bound (more negative energy) than one in the \( n = 6 \) shell. A more negative energy value indicates a stronger binding to the nucleus. 3. **Conclusion**: - The incorrect statement is **Statement 4**. It misinterprets the relationship between energy and binding strength. ### Final Answer: The conclusion that is not correct is: "For \( n = 1 \), the electron has more negative energy than it does for \( n = 6 \), indicating that the electron is loosely bound in the smallest allowed orbit."
To determine which conclusion based on the equation \( E = -2.178 \times 10^{-18} \, \text{J} \left( \frac{Z^2}{n^2} \right) \) is not correct, we will analyze each statement one by one. ### Step-by-Step Solution: 1. **Understanding the Equation**: - The equation represents the energy of an electron in a hydrogen-like atom, where \( Z \) is the atomic number and \( n \) is the principal quantum number (energy level). - The negative sign indicates that the energy is lower (more negative) when the electron is bound to the nucleus compared to when it is free (at infinity). ...
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