Question

Point out every mistake with the following set of quantum numbers for an electron in a hydrogen atom, and then write a new, valid set of quantum numbers with the magnetic value, and find the energy of that electron for the new quantum numbers you picked using -13.6 eV for the hydrogen ground-state energy: (0,1,-2,-3)

Answer 1

Quantum numbers are represented by (n,l,m,s)

n=principal quantum number

l=azimuthal quantum number(0 to n-1)

m=magnetic quantum number(+l to -l)

s=spin quantum number(+1/2 or -1/2)

n=0

n can't be zero it does not represent any orbit for h atom

l=1 is not valid as l can not be greater than n

m=-2 is also not possible as magnitude of m can't be greater than l

m= +1/2 or -1/2 so m=-3 is invalid.

Now we write new set of quantum number for n=1

l=0 as l starts from 0 and ends at n-1

m=0

s=1/2 we choose + sign for up spin.

Hence set of quantum number is(1,0,0,+1/2)

Energy = -13.6/n^2 EV

n=1 therefore energy is -13.6 eV.