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What is the shape of 1s and 2s orbital ....

What is the shape of 1s and `2s` orbital .Give two point of difference between `1s` and `2s` orbital

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### Step-by-Step Solution: 1. **Shape of 1s and 2s Orbitals**: - Both the 1s and 2s orbitals are spherical in shape. This spherical shape is a characteristic of all s orbitals, regardless of the principal quantum number (n). The shape is determined by the azimuthal quantum number (l), which is 0 for s orbitals. 2. **Difference Based on Energy**: - The energy of an orbital can be determined using the formula \( n + l \), where \( n \) is the principal quantum number and \( l \) is the azimuthal quantum number. - For the 1s orbital: - \( n = 1 \) - \( l = 0 \) - Therefore, \( n + l = 1 + 0 = 1 \) - For the 2s orbital: - \( n = 2 \) - \( l = 0 \) - Therefore, \( n + l = 2 + 0 = 2 \) - Since the value of \( n + l \) is higher for the 2s orbital, it has higher energy compared to the 1s orbital. Thus, the energy of the 1s orbital is less than that of the 2s orbital. 3. **Difference Based on Number of Nodes**: - The number of nodes in an orbital can be calculated using the formula \( n - 1 \). - For the 1s orbital: - \( n = 1 \) - Therefore, the number of nodes = \( 1 - 1 = 0 \) (indicating there are no nodes in the 1s orbital). - For the 2s orbital: - \( n = 2 \) - Therefore, the number of nodes = \( 2 - 1 = 1 \) (indicating there is one node in the 2s orbital). - Hence, the 1s orbital has no nodes, while the 2s orbital has one node. ### Summary of Differences: 1. **Energy**: The energy of the 1s orbital is less than that of the 2s orbital. 2. **Number of Nodes**: The 1s orbital has 0 nodes, while the 2s orbital has 1 node.

### Step-by-Step Solution: 1. **Shape of 1s and 2s Orbitals**: - Both the 1s and 2s orbitals are spherical in shape. This spherical shape is a characteristic of all s orbitals, regardless of the principal quantum number (n). The shape is determined by the azimuthal quantum number (l), which is 0 for s orbitals. 2. **Difference Based on Energy**: - The energy of an orbital can be determined using the formula \( n + l \), where \( n \) is the principal quantum number and \( l \) is the azimuthal quantum number. - For the 1s orbital: ...
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CENGAGE CHEMISTRY ENGLISH-ATOMIC STRUCTURE-Concept Applicationexercise(4.3)
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