The letters n, I and m proposed by Bohr, Sommerfeld and Zeeman respectively for quantisation of angular momentum in classical physics were later on obtained as the results of solution of Schrödinger wave equation based on quantum mechanics. The term n, l, m were named as principal quantum number, azimuthal quantum number and magnetic quantum number respectively. The fourth quantum number i.e., spin quantum number, s was given by Uhlenback on the basis of two spins of electrons. The first two quantum numbers also decides the nodes of an orbital. The numerical value Ψ$$4$$,$$3$$,$$0$$ denotes : The angular momentum of $$3p-orbitals$$ in terms of ħħ$$=h2$$π is: Which statement about energy level in $$H-atom$$ is correct?

Question

The letters n, I and m proposed by Bohr, Sommerfeld and Zeeman respectively for quantisation of angular momentum in classical physics were later on obtained as the results of solution of Schrödinger wave equation based on quantum mechanics. The term n, l, m were named as principal quantum number, azimuthal quantum number and magnetic quantum number respectively. The fourth quantum number i.e., spin quantum number, s was given by Uhlenback on the basis of two spins of electrons. The first two quantum numbers also decides the nodes of an orbital.  The numerical value Ψ$$4$$,$$3$$,$$0$$ denotes :  The angular momentum of $$3p-orbitals$$ in terms of ħħ$$=h2$$π is: Which statement about energy level in $$H-atom$$ is correct?

Infinity Learn · Accepted Answer

Ψ represents an orbital and Ψ$$4$$,$$3$$,$$0$$ has $$n=4$$,$$l=3$$, i.e., $$4f-orbital$$.  Angular momentum in an orbital $$=l(l+1)$$⋅$$h2$$π$$=1(1+1)$$⋅$$h2$$π$$=2$$ħall $$Sub-shells$$ of a shell in $$H-atom$$ possess same energy level, i.e.,$$($$ l $$)$$ does not specify for the energy level of an orbital in $$H-atom$$.

Quantum mechanical model of the atom

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$The numerical value Ψ_{4, 3, 0} denotes :$

$Ψ represents an orbital and Ψ_{4, 3, 0} has n = 4, l = 3, i.e., 4 f -orbital.$

$The angular momentum of 3 p -orbitals in terms of ħ (ħ = \frac{h}{2 π}) is:$

$Angular momentum in an orbital = \sqrt{l (l + 1)} \cdot \frac{h}{2 π} = \sqrt{1 (1 + 1)} \cdot \frac{h}{2 π} = \sqrt{2} ħ$

Which statement about energy level in H-atom is correct?

all Sub-shells of a shell in H-atom possess same energy level, i.e.,( $l$ ) does not specify for the energy level of an orbital in H-atom.

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Quantum mechanical model of the atom

Unlock the full solution & master the concept.

The numerical value Ψ4,3,0 denotes :

Ψ represents an orbital and Ψ4,3,0 has n=4,l=3, i.e., 4f-orbital.

The angular momentum of 3p-orbitals in terms of ħħ=h2π is:

Angular momentum in an orbital =l(l+1)⋅h2π=1(1+1)⋅h2π=2ħ