How many electrons in an atom could have these sets of quantum numbers?n=2 --> number electrons =?

quantum-numbers
electrons-atom

#1

How many electrons in an atom could have these sets of quantum numbers?

n=2 --> number electrons = ?
n=5, l=2 --> number electrons= ?
n=7, l=1, ml=-1 --> number electrons= ?

Concepts and reason
Quantum numbers describes the energy states and orbitals of the atom. Quantum numbers are classified in to four types. They are,

  1. Principle quantum number
  2. Angular momentum quantum number
  3. Magnetic quantum number
  4. Spin quantum number

Fundamentals
Principle quantum number is denoted with n and it describes the energy level of the orbital. n values are started from 1, 2, 3, so on. Calculate the number of electron in n shell by using the formula image.
Angular quantum number is denoted with l and its describes the shape of the orbital

  • If l=0 then sublevel is s
  • If l=1 then sublevel is p
  • If l=2 the sublevel is d
  • If l=3 the sublevel is f

Magnetic quantum number is denoted with l and it describes the orientation of the orbital in space. Number of orbitals possible for the given n value is calculated by using image

Answer:
N value is 2. So, calculate the number of electron by using following formula image
image
Thus, the number electrons present in n = 2 shell are 8 electrons.

image

Thus, the number electrons present in image are 10 electrons.

image means 5d sublevel. In this level five orbitals are present. Each orbital can accommodate two electrons. So, number of electrons present in image is 10 electrons.

image

Thus, the number electrons present in image are 2 electrons.