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Quantum Numbers

The angular w...

Question

The angular wave function depends upon which quantum numbers?

A

n

and

l

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B

l

and

m

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C

l

only

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D

m

only

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Solution

The correct option is C $l$ and $m$
The quantum numbers, $l$ and $m$ decide the shape of the electron cloud and its spatial orientation. They thus decide the angular wave function of the orbital.

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Q. The wave function

ψ_{n, l, m}

is a mathematical function whose value depends upon spherical polar coordinates

(r, θ, ϕ)

of the electron and characterized by the quantum numbers n, l and

m_{l}

. Here r is distance from nucleus,

θ

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ϕ

is azimuth. In the mathematical functions given in the table, Z is atomic number and

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Q. Assertion :In hydrogen and hydrogen like species, orbital energy depends only on the quantum number n whereas in multi-electron atom it depends on quantum numbers n and l. Reason: The principal quantum number determines the size and the energy of the orbital.

Q. The wave function

ψ_{n, l, m}

is a mathematical function whose value depends upon spherical polar coordinates

(r, θ, ϕ)

of the electron and characterized by the quantum numbers n, l and

m_{l}

. Here r is distance from nucleus,

θ

is colatitude and

ϕ

is azimuth. In the mathematical functions given in the table, Z is atomic number and

a_{0}

is Bohr radius.

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b. n=3, l=1, m=+1
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