Physics, 27.07.2019 23:30 phancharamachasm

The s orbital is spherical (nondirectional because check all that apply. check all that apply. the angular wave function for all s orbitals is a constant. the angular wave function of an s orbital varies with the principal quantum number (n. an s orbital has angular nodes. the angular wave function of an s orbital is defined by the quantum number ? . at a particular distance from the nucleus, the electron probability is the same in all directions.

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Answer from: Orlandon220

The correct statements are,

1. Angular wave function for all s orbitals is constant.

2. The angular wave function of s orbital is defined by the quantum number l.

3. At a particular distance from nucleus, the electron probability is the same in all directions.

Further Explanation:

The size, shape, energy, and orientation of an orbital depend upon four quantum numbers. These quantum numbers are,

1. Principal Quantum Number (n): It denotes the principle electron shell. The values of n are positive integer (1, 2, 3, ).

2. Angular Momentum Quantum Number (l): It represents the shape of an orbital. The value of l is an integer from 0 to $\left( {n - 1}\right)$ .

3. Magnetic Quantum Number $\left( {{m_l}}\right)$ : This quantum number represents the orientation of the orbital in space. The value of lie between ${m_l}$ to + l . The formula to calculate the value of ${m_l}$ is as follows:

${m_l}= - l,( - l + 1),.....,0,1,2,.....,(l - 1),l$

4. Electron Spin Quantum Number $({m_s})$ : It represents the direction of electron spin. Its value can be $+\frac{1}{2}$ or $- \frac{1}{2}$ .

s-orbital,

When the quantum number l of orbital is 0 then it is known as s-orbital. Also, they have zero nodes. The non zero value of quantum number l gives non-spherical shapes of the orbital. Schrodinger wave functions of s-orbitals show that they only depend on the distance from the nucleus and not on the directions because functions do not have any $\phi$ and $\theta$ in them. Therefore, the angular wave function for s-orbital is constant in all direction.

$\begin{aligned}{\psi _{1s}}\left( {r,\theta ,\phi }\right)&=\frac{1}{{\sqrt \pi }}{\left( {\frac{1}{{{a_0}}}} \right)^{3/2}}{e^{ - r/{a_0}}}\hfill\\{\psi _{2s}}(r,\theta ,\phi )&=\frac{1}{{4\sqrt {2\pi }}}{\left({\frac{1}{{{a_0}}}}\right)^{3/2}}\left({2 - \frac{r}{{{a_0}}}}\right){e^{ - r/2{a_0}}}\hfill\\\end{aligned}$

Hence the correct statements are regarding s-orbital is as follows:

1. The angular wave function for all s orbitals is a constant.

2. The angular wave function of an s orbital is defined by the quantum number l.

3. At a particular distance from nucleus, the electron probability is the same in all directions.

Learn more:

1. Classification of the solubility gases.

2. Calculation of volume of gas:

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Structure of atom

Keywords: s orbitals, l values, angular momentum quantum number, principal quantum number, magnetic quantum number, electron spin quantum number, s orbital is spherical.

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