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Statement-1. The number of radial nodes ...

Statement-1. The number of radial nodes in 3s and 4p orbitals is not equal.
Statement-2 The number of radial nodes in any orbital depends upon the values of 'n' and 'l' which are different for 3s and 4p orbitals

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-5

B

Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-2

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both statements regarding the number of radial nodes in the 3s and 4p orbitals. ### Step-by-Step Solution: 1. **Understanding Radial Nodes**: - Radial nodes are regions in an atom where the probability of finding an electron is zero. They are spherical in shape. - The formula to calculate the number of radial nodes in an orbital is given by: \[ \text{Number of Radial Nodes} = n - l - 1 \] where \( n \) is the principal quantum number and \( l \) is the azimuthal quantum number. 2. **Identify Quantum Numbers for 3s and 4p Orbitals**: - For the **3s orbital**: - \( n = 3 \) - \( l = 0 \) (since s orbitals have \( l = 0 \)) - For the **4p orbital**: - \( n = 4 \) - \( l = 1 \) (since p orbitals have \( l = 1 \)) 3. **Calculate Radial Nodes**: - For **3s orbital**: \[ \text{Radial Nodes} = 3 - 0 - 1 = 2 \] - For **4p orbital**: \[ \text{Radial Nodes} = 4 - 1 - 1 = 2 \] 4. **Comparison of Radial Nodes**: - Both the 3s and 4p orbitals have **2 radial nodes**. Therefore, the statement that the number of radial nodes in 3s and 4p orbitals is not equal is **incorrect**. 5. **Analyzing Statement-2**: - Statement-2 claims that the number of radial nodes depends on the values of \( n \) and \( l \), which is true. - However, it also states that these values are different for 3s and 4p orbitals. Since we found that both orbitals have the same number of radial nodes (2), this part of the statement is also **incorrect**. 6. **Conclusion**: - Both statements are incorrect. Therefore, the correct option is that both statements are false. ### Final Answer: Both Statement-1 and Statement-2 are incorrect. ---

To solve the question, we need to analyze both statements regarding the number of radial nodes in the 3s and 4p orbitals. ### Step-by-Step Solution: 1. **Understanding Radial Nodes**: - Radial nodes are regions in an atom where the probability of finding an electron is zero. They are spherical in shape. - The formula to calculate the number of radial nodes in an orbital is given by: \[ ...
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