how many electrons in an atom have quantom number n=4 and m=-1/2
Answers
n - Principal Quantum number which determines the size of the the orbital. It starts from 1 to infinity.
l - Angular Quantum number defines the shape of the orbital. It starts from 0 to n.
m - Magnetic Quantum number determines the orientation of the orbital in space. It goes from -l to +l.
s - Spin Quantum number is an intrinsic angular momentum property of the electron. It has only two values +1/2 and -1/2.
So according to the problem:
n=4;
l=0,1,2,3;
So, for each l value, corresponding m value will have 2 electons but s is restricted to -1/2 only; so only half the number of electrons each l value can contain.
For l=0 : m=0 — 1 electron
For l=1 : m=-1,0,1 — 3 electrons
For l=2 : m=-2,-1,0,1,2 — 5 electrons
For l=3 : m=-3,-2,-1,0,1,2,3 — 7 electons
Thus, adding up: total electons in n=4 and s=-1/2 are = 16 electrons.
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Answer:
the answer is 16.
Explanation:
for nth orbital possible values of the azimuthal quantum number, I are from 0 to (n-1). total of n values.
in n=4 and l=0,1,2,3.
magnetic quantum number have values from -l to +l and total of 2l +1 value
for n=4 possible values of 1 and ml are.,
ml=0,for l=0.total ml value =1.
ml=-1,0,1 for l=1,total ml value =3.
ml=-2,-1,0,1,2 for l=2,total ml value =5.
ml=-3,-2,-1,0,1,2,3 for l=3.total ml value =7.
total number of orbitals = total values of ml.
for n=4.
therefore1+3+5+7 = 16 orbitals.each orbital can occupy maximum of 2 electrons.
number of electrons =2.16=32.