The next two questions are related: 5. How many distinct (n,l,m) states of the h

Question

The next two questions are related:
5. How many distinct (n,l,m) states of the hydrogen atom with n = 3 are there? Neglect
electron spin.
a. 1 distinct state
b. 5 distinct states
c. 9 distinct states


6. Which statement about the energies of the (n,l,m) states of the hydrogen atom with n = 3 is
correct?
a. They are all equal to -1.51 eV.
b. The highest (most positive) energy is equal to -1.51 eV, the others are all smaller.
c. At least one energy is equal to -2.44 eV.
d. At least one energy is equal to +3.55 eV.
e. States with larger l have higher energies.

Explanation / Answer

5. For a given n, l can have values upto n-1 For a given l, m can have 2l+1 values from -l to l (3, __, __) (3,0,0) (3,1,0) (3,1,1) (3,1,-1) (3,2,0) (3,2,1) (3,2,-1) (3,2,2) (3,2,-2) 9 possible! 6. E = -13.6 /n^2 = -13.6/9 = -1.51eV Obviously all these electrons have the same energy, acc to definition of principal quantum number.

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