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Shapes of Orbitals and Nodes

Which of the ...

Question

Which of the following orbitals have no spherical nodes?

1 s

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2 s

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2 p

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3 p

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Solution

The correct options are
A $2 p$
B $1 s$
Number of spherical nodes for an orbital $n - l - 1$
where, n is principal quantum number
l is Azimuthal quantum number
For s orbital $l = 0$
p orbital $l = 1$
d orbital $l = 2$ and so on.
Now ,
$1 s \to n = 1, l = 0$
$⟹ n - l - 1 = 0 = 1 - 0 - 1 = 0$
$2 p \to n = 2, l = 1$
$⟹ n - l - 1 = 0 = 2 - 1 - 1 = 0$
$2 s \to n = 2, l = 0$
$⟹ n - l - 1 = 0 = 2 - 0 - 1 = 1$
$3 p \to n = 3, l = 1$
$⟹ n - l - 1 = 0 = 3 - 1 - 1 = 1$
Therefore 1s and 2p orbitals have no spherical nodes.

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