Question

Q15.An electron in a hydrogen atom is described by the quantum numbers: n=8 and m_(l)=4 What are the possible values for the orbital quantum number?​

Answer 1

Explanation:

The answer to the asked question is explained in the picture attached.

Answer 2

Answer:

The possible values for the orbital quantum number are $4,5,6,7.$

Explanation:

• Angular momentum quantum number can have value from $0$ to $n-1.$

                           $n-1 = 8-1$

                                   $= 7$

                            $l = 0$ to $7$

                         $l = 0,1,2,3,4,5,6,7$

• With magnetic quantum number $-l$ to $+l.$

• Here, Principal quantum number $(n) = 8$

• Angular Momentum number $(m_{l} ) = 4$

It means magnetic quantum number varies from $= -4$  to  $+4$

For $l= 0$                          $m_{l} = 0$

For $l =1$                            $m_{l} = -1$ to $+1$

For $l = 2$                           $m_{l} = -2$  to $+2$

For $l = 3$                          $m_{l} = -3$ to $+3$

For  $l= 4$                           $m_{l} = -4$ to $+4$

For $l = 5$                             $m_{l} =-5$ to $+5$

For $l = 6$                             $m_{l} = -6$ to $+6$

For $l = 7$                             $m_{l} = -7$ to $+7$

$m_{l} =4$ is included only  for  $l = 4,5,6,7$.

Therfore,possible values for the orbital quantum numbers $4,5,6,7$.

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