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The quantum state of a particle can be specified by giving a complete set of quantum numbers (n,l, ml, ms). How many different quantum states are possible if the principal quantum number is n = 2? To find the total number of allowed states, first, write down the allowed orbital quantum numbers l, and then write down the number of allowed values of ml for each orbital quantum number. Sum these quantities, and then multiply by 2 to account for the two possible orientations of spin. Express your answer as an integer.

Answer :

mavila18

Answer:

number of quantum states =  8

Explanation:

To find the total number of allowed states you take into account the following relations:

[tex]l=n-1\\\\m_l=-l,-(l-1),...,0,,,,(l-1),l[/tex]

in this case you have:

[tex]n=2\\\\l=0,1\\\\m_0=0\\\\m_1=-1,0,1[/tex]

furthermore, for each n,l,ml quantum state you have two additional states due to the spin of the electrons.

then, you have (n,l,ml) = (2,0,0), (2,1,-1), (2,1,0), (2,1,1) and with the spin:

number of quantum states = 2*(1+3) = 8

The number of quantum states for the given principal quantum numbers is 8.

The given problem is based on the quantum state. The quantum states are specified by values of attributes such as charge and spin, and are characterized by particular energy level.

To find the total number of allowed states you take into account the following relations:

l = n - 1

Here, n is the principal quantum number.

m' = -l, -(l - 1) ...........0.........( l -1 ), l

Here, m' is the magnetic quantum number.

Since we have, n =2.

Which means,

l = 2 - 1

l =1

So, the value of magnetic quantum is given as,

m' = -0, -(0-1) .....................(0-1),0

m' = -1, 0 , 1

Also, for each n, l, ml quantum state you have two additional states due to the spin of the electrons.

For the set of principal quantum numbers (n, l, ml) = (2,0,0), (2,1,-1), (2,1,0), (2,1,1) and with the spin:

So, the number of quantum states is,

=  2*(1+3) = 8

Thus, we can conclude that the number of quantum states for the given principal quantum numbers is 8.

Learn more about the quantum states here:

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