Chapter 5, Problem 36A

Interpretation Introduction

Interpretation: The given subshells need to be arranged in order of increasing energy.

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 36A

  $2s<3p<4s<3d$

Explanation of Solution

The given orbitals are $3d$ , $2s$ , $4s$ and $3p$ .

The energy of an orbital depends on the four quantum numbers. Here, as the principal quantum number increases, energy also increases, thus, a subshell with a minimum value of the principal quantum number will have minimum energy. Thus, 2s will have minimum energy.

When electrons are filled 3d is always filled before 4s this is due to the high energy of 3d orbitals as compared to 4s. Due to less energy of 4s, it can be filled first.

Thus, the energy of 3d is more than 4s .

Therefore, the order of increasing energy in the atomic subshell will be:

  $2s<3p<4s<3d$

Conclusion

Therefore, the order of increasing energy is as follows:

  $2s<3p<4s<3d$