Question

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For atoms with Principle Quantum number 4, what are the possible values for (Secondary Quantum Number) and m (Magnetic Quantum Number)?

Answer 1

Answer:

Step 1: Explanation:

In atoms, there are a total of four quantum numbers: the principal quantum number (n), the orbital angular momentum quantum number (l), the magnetic quantum number (m_l), and the electron spin quantum number (m_s).

The Principal Quantum Number (n): The principal quantum number ( n) designates the principal electron shell.It can be any positive integer starting at 1.( i.e n=1,2,3,4) as n=1 designates the first principal shell (the innermost shell).

The Orbital Angular Momentum Quantum Number (l):

The orbital angular momentum quantum number l determines the shape of an orbital.The value of l can be zero. It can also be a positive integer, it always one less than the principal quantum number (n-1).

i.e l =0,1,2,3.....(n-)

The Magnetic Quantum Number (m_l):

The magnetic quantum number (m_l) determines the number of orbitals and their orientation within a subshell. Consequently, its value depends on the orbital angular momentum quantum number (l). Given a certain l (ml) is an interval ranging from ( -l to +l ).

Step 2: Solution

since we know for a given value of n, the value of l must be 0 to n-1

so if n= 4 then l= 0,1,2,3

Now we know for a given value of l, the value of m_l must be -l to +l

so if l= 0 then m_l= 0

if l= 1 then m_l= -1,0,+1

if l= 2 then m_l= -2,-1,0,+1,+2

if l= 3 then m_l= -3, -2,-1,0,+1,+2 ,+3

So in short all possible values

if n =4 , then l = 0,1,2,3 and m_l = -3, -2,-1,0,+1,+2 ,+3