The maximum possible values of magnetic orbital quantum number ( $m_{l})$ are

(2 l + 1)

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2 l

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(2 l - 1)

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zero

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Solution

The correct option is A $(2 l + 1)$
The principal quantum number n, belongs to the principal shell z $(K, L, M, . . . .)$ which is occupied by an electron and can be any positive integer $(n = 1, 2, 3, 4, . . . . . . . .)$ . Its location is further narrowed down by the angular momentum quantum number l, corresponding to the subshell and its general shape. The value of l is dependent on the value of $n (l = 0, 1, 2, . . . . . . . . . ., n - 1)$ . The values of l correspond to specific subshells i.e. l = 0 for s; l = 1 for p; l = 2 for d; l = 3 for f.
The magnetic quantum number( $m_{l}$ ), further divides these subshells into orbitals and gives orientation of these orbitals in space. The number of orbitals can be determined from the angular momentum quantum number l and the maximum possible values of $m_{l}$ can be determined from number of orbitals given by, $(2 l + 1) .$

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Q. Electrons are precisely distinguished by what are known as quantum numbers. i.e., n, l, m_l and m_s. n defines the shell. There are n subshells in the n^th shell. There are (2l + 1) orbitals of each type in subshell that is, one s-orbital (l = 0), three p orbitals (l = 1), five d orbitals (l = 2) and seven f orbitals (l = 3) per subshell. m_l designates the orientation of the orbital and for a given value of l, m_l has (2l + 1) values. m_s refers to orientation of spin of the electrons.

इलेक्ट्रॉनों को परिशुद्ध रूप से क्वाण्टम संख्याओं अर्थात् n, l, m_l एवं m_s द्वारा विभेदित किया जाता है। n कोश को परिभाषित करता है। n^th कोश में n उपकोश होते हैं। एक उपकोश में प्रत्येक प्रकार के (2l + 1) कक्षक होते हैं जैसे प्रति उपकोश में एक s-कक्षक (l = 0), तीन p कक्षक (l = 1), पाँच d कक्षक (l = 2) तथा सात f कक्षक (l = 3) होते हैं। m_l कक्षक के अभिविन्यास को निर्धारित करता है तथा l के दिए गए मान के लिए m_l के मान (2l + 1) होते हैं। m_s इलेक्ट्रॉनों के चक्रण के अभिविन्यास का निर्धारण करता है।
Q. Total number of orbitals possible in 4^th shell is

प्रश्न -4^th कोश में संभव कक्षकों की कुल संख्या है

Q. Factorise:

(2 l + m)^{2} - 8 l m

Q. For a given value of

l

, the total number of 'm' values are

2 l + 1

Q. Assertion :Each principal level of quantum number

^{'} n^{'}

contains a total of

^{'} n^{'}

sub levels. Reason: Each orbital can hold two electrons and each sub level of quantum number

^{'} l^{'}

contains a total of

(2 l + 1)

orbitals.

Q. Assertion :For l=2,

m_{1}

can be -2, -1, 0, +1 and +2 . Reason: For a given value of l , (2l+1) values of

m_{1}

are possible.

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The maximum possible values of magnetic orbital quantum number (ml) are

The maximum possible values of magnetic orbital quantum number ( $m_{l})$ are