Question

Find all possible values of the following for a hydrogen atom in a 3d state.

I have the value of L as 2.57e-34 which is correct.

L_z. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks. Use the following as necessary: h(bar))

There are 4 boxes and the 2nd and 3rd are 1 and 2 but i cannot get the first and fourth boxes.

θ. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

there are 8 boxes for this part.

Thank you!

Answer 1

first to find L value , with the follwoing given data ,

considering all possible values of the following for a hydrogen atom in a 3d state ,

For 3d state ,

We can write n values and ‘l’ values are

n = 3 and = 2

then for L we have

L = ( + 1 ) ђ

L = 2 ( 2 + 1 ) ђ

L = 2 X 3 ђ

L = 6 ђ

But we have ђ = h / 2 π

Then L = 6 X h / 2 π

L = 6 X 6.67 X 10^-34 / 2 X 3.14

L = 2.57 X 10^-34 J.s

Next for m _Ɩ can have the values are -2 , - 1 , 0, 1 , 2

Then simply we can write as

L_Z values are -2 ђ , - 1 ђ , 0 ,1 ђ, 2 ђ

But we have cosθ = 2 ђ / L

cosθ = - 2 ( h / 2 π )/ L

Then substituting L_Z and L values separately

cosθ = L_Z / L

cosθ = L_Z / L

cosθ = - 2 X 6.67 X 10^-34 / 2 X 3.14 X 2.57 X 10^-34

cosθ = - 0.82

θ = cos^-1 ( - 0.82 )

θ = 145.08⁰

similarly substituting like above

for - 1 ђ , 0 ,1 ђ, 2 ђ

the corresponding θ value for - 1 ђ is   114⁰

the corresponding θ value for 0 is   90⁰

the corresponding θ value for 1 ђ is   65.9⁰

the corresponding θ value for 2 ђ is   35.31⁰