STATEMENT-1: The angular momentum of d-orbitals is `sqrt6(h)/(2pi)` STATEMENT 2 : Angular momentum of electron in orbit is `mvr=(nh)/(2pi)`
A
If both the statement are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B
If both the statements are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C
If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D
If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE
Text Solution
AI Generated Solution
The correct Answer is:
To determine the validity of the given statements, we need to analyze each statement step by step.
### Solution Steps:
1. **Understanding Statement 1**:
- The statement claims that the angular momentum of d-orbitals is given by the formula \(\sqrt{6} \frac{h}{2\pi}\).
- The angular momentum \(L\) of an electron in an orbital can be calculated using the formula:
\[
L = \sqrt{l(l + 1)} \frac{h}{2\pi}
\]
- Here, \(l\) is the azimuthal quantum number, which is 2 for d-orbitals.
2. **Calculating Angular Momentum for d-orbitals**:
- Substituting \(l = 2\) into the formula:
\[
L = \sqrt{2(2 + 1)} \frac{h}{2\pi} = \sqrt{2 \cdot 3} \frac{h}{2\pi} = \sqrt{6} \frac{h}{2\pi}
\]
- Thus, Statement 1 is correct.
3. **Understanding Statement 2**:
- The second statement claims that the angular momentum of an electron in an orbit is given by \(mvr = \frac{nh}{2\pi}\).
- This is a statement derived from Bohr's model of the atom, which quantizes the angular momentum of electrons in orbits.
4. **Verifying Statement 2**:
- According to Bohr's theory, the angular momentum \(L\) of an electron in a circular orbit is quantized and given by:
\[
L = mvr = \frac{nh}{2\pi}
\]
- This means that for any electron in a defined orbit, this relationship holds true, confirming that Statement 2 is also correct.
5. **Determining the Relationship Between the Statements**:
- While both statements are true, Statement 2 does not explain Statement 1. Statement 1 pertains specifically to the angular momentum of d-orbitals, while Statement 2 is a general statement about the angular momentum of electrons in any orbit.
### Conclusion:
- Both statements are true, but Statement 2 is not the correct explanation for Statement 1.
### Final Answer:
- Both statements are true, but Statement 2 is not the correct explanation of Statement 1.
