Respuesta :
Answer:
The S orbital is spherical because at a particular distance from the nucleus, the electron probability is the same in all directions.
Further details:
S orbital is spherical because the proton-attraction is uniform all along around the nucleus; hence the probability distribution is uniform radially, which make its orbital spherical.
Nuclear orbital:
In nuclear hypothesis and quantum mechanics, a nuclear orbital is a numerical capacity that depicts the wave-like conduct of either one electron or a couple of electrons in an atom. This capacity can be utilized to compute the probability of finding any electron of a molecule in a particular district around the particle's core.
S Orbital:
The s orbital is a circularly molded region describing where an electron can be found, inside a specific level of probability. The state of the orbital relies upon the quantum numbers related with an energy state. All s orbitals have l = m = 0, however the estimation of n can fluctuate.
State of S orbital:
An s orbital is roundly symmetric around the core of the molecule, similar to an empty ball made of rather fluffy material with the core at its middle. As the energy levels increment, the electrons are found further from the core, so the orbitals get greater. The request for size is 1s < 2s < 3s <.
Answer details:
Subject: Physics
Level: High school
Keywords:
• Atomic orbitals
• S orbital
• Shape of S orbital
• Why s orbital is spherical
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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 [tex]\left( {n - 1}\right)[/tex] .
3. Magnetic Quantum Number [tex]\left( {{m_l}}\right)[/tex]: This quantum number represents the orientation of the orbital in space. The value of lie between [tex]{m_l}[/tex] to [tex]+ l[/tex] . The formula to calculate the value of [tex]{m_l}[/tex] is as follows:
[tex]{m_l}= - l,( - l + 1),.....,0,1,2,.....,(l - 1),l[/tex]
4. Electron Spin Quantum Number[tex]({m_s})[/tex] : It represents the direction of electron spin. Its value can be [tex]+\frac{1}{2}[/tex] or[tex]- \frac{1}{2}[/tex] .
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 [tex]\phi[/tex] and [tex]\theta[/tex] in them. Therefore, the angular wave function for s-orbital is constant in all direction.
[tex]\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}[/tex]
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.
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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.
