Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (ℓ), the magnetic quantum number (mℓ), and the spin quantum number (ms) have strict rules which govern the possible values. Identify allowable combinations of quantum numbers for an electron. Select all that apply.
n=2, l=1,ml=-1,ms=-1
n=3, l=2,ml=1, ms=+1/2
n=5, l=3, ml=-1, ms=-1/2
n=5, l=5, ml=1, ms=+1/2
n=3, l=-2, ml=1, ms=+1/2
n=4, l=2, ml=3, ms=+1/2
oops Geethica.
ml can be -l on the lowest to +l on the highest so ml of 3 is not possible. Your last answer is not possible.
The principal quantum number n of Group 14 elements increases in the order C > Si > Ge > Sn > Pb. Which amongst these elements will have the least electron affinity ?
Question 2Select one:
a.
Sn
b.
Pb
c.
Ge
d.
C
To identify allowable combinations of quantum numbers for an electron, we need to consider the rules that govern these numbers:
1. The principal quantum number (n): It determines the energy level or shell of the electron. Allowed values for n are positive integers (1, 2, 3, etc.).
2. The angular momentum quantum number (ℓ): It signifies the shape of the electron's orbital. Allowed values for ℓ range from 0 to n-1.
3. The magnetic quantum number (mℓ): It indicates the orientation of the orbital within a particular subshell. The range of allowed values for mℓ is from -ℓ to +ℓ.
4. The spin quantum number (ms): It describes the spin state of the electron. Only two values are possible: +1/2 for "spin-up" and -1/2 for "spin-down."
Now, let's analyze each combination of quantum numbers:
1. n=2, ℓ=1, mℓ=-1, ms=-1
This is an allowable combination as it satisfies the rules mentioned above.
2. n=3, ℓ=2, mℓ=1, ms=+1/2
This is also an allowable combination as it follows the rules.
3. n=5, ℓ=3, mℓ=-1, ms=-1/2
This is an allowable combination as it satisfies the rules.
4. n=5, ℓ=5, mℓ=1, ms=+1/2
This combination violates the rule for ℓ. For a given n, the maximum allowed value of ℓ is (n-1). Therefore, ℓ cannot be equal to n in this case.
5. n=3, ℓ=-2, mℓ=1, ms=+1/2
The value of ℓ cannot be negative, so this combination is not allowable.
6. n=4, ℓ=2, mℓ=3, ms=+1/2
The value of mℓ cannot exceed the maximum allowed value, which is ℓ. Therefore, this combination is not allowed.
Based on the analysis, the allowable combinations of quantum numbers for an electron are:
- n=2, ℓ=1, mℓ=-1, ms=-1
- n=3, ℓ=2, mℓ=1, ms=+1/2
- n=5, ℓ=3, mℓ=-1, ms=-1/2
So, the correct options are:
n=2, ℓ=1, mℓ=-1, ms=-1
n=3, ℓ=2, mℓ=1, ms=+1/2
n=5, ℓ=3, mℓ=-1, ms=-1/2
Allowable combinations are
n=3, l=2,ml=1, ms=+1/2
n=5, l=3, ml=-1, ms=-1/2
n=4, l=2, ml=3, ms=+1/2
Combinations not allowed
n=2, l=1,ml=-1,ms=-1
because ms has to -1/2 or +1/2
n=5, l=5, ml=1, ms=+1/2
because n and l cannot be equal
n=3, l=-2, ml=1, ms=+1/2
because l cannot be negative.