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Among the following molecular orbitals h...

Among the following molecular orbitals how many have at least one nodal plane? `sigma^ast1s`,`sigma2s`,`sigma^ast2p_z`,`pi2p_x`,`pi^ast2p_y`, `sigma 2p_z`

A

4

B

5

C

2

D

6

Text Solution

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The correct Answer is:
To determine how many of the given molecular orbitals have at least one nodal plane, we need to analyze each molecular orbital provided in the question. A nodal plane is a region in a molecular orbital where the probability of finding an electron is zero. ### Step-by-Step Solution: 1. **Identify the Molecular Orbitals**: The molecular orbitals given are: - \( \sigma^* 1s \) - \( \sigma 2s \) - \( \sigma^* 2p_z \) - \( \pi 2p_x \) - \( \pi^* 2p_y \) - \( \sigma 2p_z \) 2. **Analyze Each Molecular Orbital**: - **\( \sigma^* 1s \)**: This is an antibonding orbital formed from the overlap of 1s orbitals. It has **one nodal plane** due to the nature of antibonding orbitals. - **\( \sigma 2s \)**: This is a bonding orbital formed from the overlap of 2s orbitals. It has **no nodal planes**. - **\( \sigma^* 2p_z \)**: This is an antibonding orbital formed from the overlap of 2p orbitals. It has **one nodal plane**. - **\( \pi 2p_x \)**: This is a bonding orbital formed from the side-on overlap of 2p orbitals. It has **one nodal plane**. - **\( \pi^* 2p_y \)**: This is an antibonding orbital formed from the side-on overlap of 2p orbitals. It has **two nodal planes**. - **\( \sigma 2p_z \)**: This is a bonding orbital formed from the overlap of 2p orbitals. It has **no nodal planes**. 3. **Count the Molecular Orbitals with Nodal Planes**: - \( \sigma^* 1s \): 1 nodal plane - \( \sigma 2s \): 0 nodal planes - \( \sigma^* 2p_z \): 1 nodal plane - \( \pi 2p_x \): 1 nodal plane - \( \pi^* 2p_y \): 2 nodal planes - \( \sigma 2p_z \): 0 nodal planes Now, we count the orbitals with at least one nodal plane: - \( \sigma^* 1s \) (1) - \( \sigma^* 2p_z \) (1) - \( \pi 2p_x \) (1) - \( \pi^* 2p_y \) (2) Total = 4 molecular orbitals with at least one nodal plane. ### Final Answer: The number of molecular orbitals that have at least one nodal plane is **4**. ---
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Comprehension given below is followed by some multiple choice question, Each question has one correct options. Choose the correct option. Molecular orbitals are formed by the overlap of atomic orbitals. Two atomic orbitals combine to form two molecular orbitals called bonding molecular orbital (BMO) and anti-bonding molecular orbital (ABMO). Energy of anti-bonding orbital is raised above the parent atomic orbitals that have combined and hte energy of the bonding orbital is lowered than the parent atomic orbitals. energies of various molecular orbitals for elements hydrogen to nitrogen increase in the order sigma1s lt sigma^(star)1sltsigma^(star)2slt((pi2p_(x))=(pi2p_(y)))ltsigma2p_(z)lt(pi^(star)2p_(x) = pi^(star)2p_(y))ltsigma^(star)2p_(z) and For oxygen and fluorine order of enregy of molecules orbitals is given below. sigma1s lt sigma^(star)1s lt sigma2s lt sigma^(star)2s lt sigmap_(z) lt (pi2p_(x) ~~ pi2p_(y)) lt (pi^(star)2p_(x)~~ pi^(star)2py) lt sigma^(star)2p_(z) Different atomic orbitalsof one atom combine with those atoms orbitals of the second atom which have comparable energies and proper orientation. Further, if the overlapping is head on, the molecular orbital is called sigma, sigma andif the overlap is lateral, the molecular orbital is called pi, pi . The molecular orbitals are filled with electrons according to the same rules as followed for filling of atomic orbitals. However, the order for filling is not the same for all molecules or their ions. Bond order is one of the most important parameters to compare the strength of bonds. In which of the following molecules, sigma2p_(z) molecular orbital is filled after pi2p_(x) and pi2p_(y) molecular orbitals?

Comprehension given below is followed by some multiple choice question, Each question has one correct options. Choose the correct option. Molecular orbitals are formed by the overlap of atomic orbitals. Two atomic orbitals combine to form two molecular orbitals called bonding molecular orbital (BMO) and anti-bonding molecular orbital (ABMO). Energy of anti-bonding orbital is raised above the parent atomic orbitals that have combined and hte energy of the bonding orbital is lowered than the parent atomic orbitals. energies of various molecular orbitals for elements hydrogen to nitrogen increase in the order sigma1s lt sigma^(star)1s lt sigma^(star)2s lt ((pi2p_(x))=(pi2p_(y))) lt sigma2p_(z) lt (pi^(star)2p_(x) = pi^(star)2p_(y)) lt sigma^(star)2p_(z) and For oxygen and fluorine order of enregy of molecules orbitals is given below. sigma1s lt sigma^(star)1s lt sigma2s lt sigma^(star)2s lt sigmap_(z) lt (pi2p_(x) ~~ pi2p_(y)) lt (pi^(star)2p_(x)~~ pi^(star)2py) lt sigma^(star)2p_(z) Different atomic orbitalsof one atom combine with those atoms orbitals of the second atom which have comparable energies and proper orientation. Further, if the overlapping is head on, the molecular orbital is called sigma, sigma andif the overlap is lateral, the molecular orbital is called pi, pi . The molecular orbitals are filled with electrons according to the same rules as followed for filling of atomic orbitals. However, the order for filling is not the same for all molecules or their ions. Bond order is one of the most important parameters to compare the strength of bonds. 67) Which of the following pair is expected to have the same bonod order?

Knowledge Check

  • Comprehension given below is followed by some multiple choice question, Each question has one correct options. Choose the correct option. Molecular orbitals are formed by the overlap of atomic orbitals. Two atomic orbitals combine to form two molecular orbitals called bonding molecular orbital (BMO) and anti-bonding molecular orbital (ABMO). Energy of anti-bonding orbital is raised above the parent atomic orbitals that have combined and hte energy of the bonding orbital is lowered than the parent atomic orbitals. energies of various molecular orbitals for elements hydrogen to nitrogen increase in the order sigma1s lt sigma^(star)1s lt sigma^(star)2s lt ((pi2p_(x))=(pi2p_(y))) lt sigma2p_(z) lt (pi^(star)2p_(x) = pi^(star)2p_(y)) lt sigma^(star)2p_(z) and For oxygen and fluorine order of enregy of molecules orbitals is given below. sigma1s lt sigma^(star)1s lt sigma2s lt sigma^(star)2s lt sigmap_(z) lt (pi2p_(x) ~~ pi2p_(y)) lt (pi^(star)2p_(x)~~ pi^(star)2py) lt sigma^(star)2p_(z) Different atomic orbitalsof one atom combine with those atoms orbitals of the second atom which have comparable energies and proper orientation. Further, if the overlapping is head on, the molecular orbital is called sigma, sigma andif the overlap is lateral, the molecular orbital is called pi, pi . The molecular orbitals are filled with electrons according to the same rules as followed for filling of atomic orbitals. However, the order for filling is not the same for all molecules or their ions. Bond order is one of the most important parameters to compare the strength of bonds. 67) Which of the following pair is expected to have the same bond order?

    A
    `C_(2)`
    B
    `B_(2)`
    C
    `O_(2)`
    D
    `Be_(2)`

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