Question

1. Heisenberg’s uncertainty principle.
2. what are the atomic numbers of the elements whose outermost electrons are represented by
   a. $3{s^1}$
   b. $3{p^5}$

Answer 1

Hint : 1) The Heisenberg uncertainty principle is a law in quantum mechanics that limits how accurately you can measure two related variables.
2) First, we have to complete the electronic configuration. We know that the sum of the superscripts in an electron configuration is equal to the number of electrons in that atom, which is in turn equal to its atomic number.

Complete Step By Step Answer:

1. Heisenberg’s uncertainty principle states that it is impossible to measure or calculate exactly, both the position and the momentum of an object. This principle is based on the wave-particle duality of matter. Since atoms and subatomic particles have very small masses, any increase in the accuracy of their positions will be accompanied by an increase in the uncertainty associated with their velocities.
   In the field of quantum mechanics, Heisenberg’s uncertainty principle is a fundamental theory that explains why it is impossible to measure more than one quantum variable simultaneously. Another implication of the uncertainty principle is that it is impossible to accurately measure the energy of a system in some finite amount of time.
   If, $\Delta x$ is the error in position measurement and $\Delta p$ is the error in the measurement of momentum, then
   $\Delta x \times \Delta p \geqslant \dfrac{h}{{4\pi }}$
   Since momentum, $p = mv$
   Then Heisenberg’s uncertainty principle formula can be alternatively written as
   $\Delta x \times \Delta \left( {mv} \right) \geqslant \dfrac{h}{{4\pi }}$ or $\Delta x \times \Delta m \times \Delta v \geqslant \dfrac{h}{{4\pi m}}$
   Where, $\Delta v$ is the error in the measurement of velocity and assuming mass remaining constant during the experiment,
   $\Delta x \times \Delta v \geqslant \dfrac{h}{{4\pi m}}$ .

a) Given outermost electrons $3{s^1}$
Then the complete electronic configuration is $1{s^2}2{s^2}2{p^6}3{s^1}$
Hence the number of electrons present in the atom of the element= $= 2 + 2 + 6 + 1 = 11$
Therefore, the atomic number of the element is 17 which is Sodium.
b) Given outermost electrons $3{p^5}$
Then the complete electronic configuration is $1{s^2}2{s^2}2{p^6}3{s^2}3{p^5}$
Hence the number of electrons present in the atom of the element= $= 2 + 2 + 6 + 2 + 5 = 17$ Therefore, the atomic number of the element is $17$ which is Chlorine ( $Cl$ ).

Note :
Note that Heisenberg’s uncertainty principle holds significant value in the quantum world. Also note that the accurate measurement of position or momentum automatically indicates larger uncertainty (error) in the measurement of the other quantity. The Heisenberg principle applies to only dual-natured microscopic particles and not to a macroscopic particle whose wave nature is very small.