Chapter 5, Problem 32A

Interpretation Introduction

Interpretation: The $1s$ , $2s$ , and $2p$ orbitals need to be sketched.

Concept introduction: An atomic orbital explains the position of an electron in an atom. An atomic orbital can be occupied by a maximum of two electrons with opposite spins. The four basic atomic orbitals are s, p, d, and f . The number of electrons in each orbital can be explained with the help of quantum numbers. There are four quantum numbers; principal quantum number ( n ), azimuthal quantum number ( l ), magnetic quantum number ( $m_l$ ), and spin quantum number ( s ). Here, for any value of n, $l=n-1$ and values of $m_l$ is from -l to + l . spin quantum number explains the spin of the electron in an atomic orbital. It can be either +1/2 or -1/2.

Answer to Problem 32A

  

Explanation of Solution

The given orbitals are 1s , 2s, and 2p . Here, 1 and 2 represent the principal quantum number ( n ). Since the value of an azimuthal quantum number is 0 for s orbital, there will be only 1 atomic orbital as a magnetic quantum number $m_l=-l\text{ to +}l$ . Here, $m_l=0$ . For p orbital, the value of an azimuthal quantum number is 1; thus, the magnetic quantum number will be -1. 0, +1. Thus, there will be 3 atomic orbitals.

The sketch can be represented as follows:

  

Conclusion

Thus, the sketch for 1s, 2s, and 2p orbital is as follows: