What is the difference between the terms orbit and orbital?
Difference between the terms orbit and orbital are as below
| Orbit | Orbital |
|---|---|
| An orbit is a well defined circular path around the nucleus in which the electrons revolve. | An orbital is the three dimensional space around the nucleus within which the probability of finding an electron is maximum (upto 90%). |
| All orbits are circular and disc like. |
Different orbitals have different shapes. |
| The concept of an orbit is not in accordance with the wave character of electrons with uncertainty principle. | The concept of an orbital is in accordance with the wave character of electrons and uncertainty principle. |
| The maximum number of electrons in any orbit is given by $$2 n^2$$ where $$n$$ is the number of the orbit. | The maximum number of electrons present in any orbital is two. |
Table-tennis ball has mass 10 g and speed of $90 \mathrm{~m} / \mathrm{s}$. If speed can be measured within an accuracy of $4 \%$, what will be the uncertainty in speed and position?
$$\begin{aligned} & \text { Given that, speed }=90 \mathrm{~m} / \mathrm{s} \\ & \qquad \text { mass }=10 \mathrm{~g}=10 \times 10^{-3} \mathrm{~kg} \\ & \text { Uncertainty in speed }(\Delta v)=4 \% \text { of } 90 \mathrm{~ms}^{-1}=\frac{4 \times 90}{100}=3.6 \mathrm{~ms}^{-1} \end{aligned}$$
From Heisenberg uncertainty principle,
$$\begin{aligned} \Delta x \cdot \Delta v & =\frac{h}{4 \pi m} \\ \text{or}\quad \Delta x & =\frac{h}{4 \pi m \Delta v} \end{aligned}$$
Uncertainty in position,
$$\begin{aligned} \Delta x & =\frac{6.626 \times 10^{-34} \mathrm{kgm}^2 \mathrm{~s}^{-1}}{4 \times 3.14 \times 10 \times 10^{-3} \mathrm{~kg} \times 3.6 \mathrm{~ms}^{-1}} \\ & =1.46 \times 10^{-33} \mathrm{~m} \end{aligned}$$
The effect of uncertainty principle is significant only for motion of microscopic particles and is negligible for the macroscopic particles. Justify the statement with the help of a suitable example.
$$\begin{aligned} &\text { If uncertainty principle is applied to an object of mass, say about a milligram }\left(10^{-6} \mathrm{~kg}\right) \text {, then }\\ &\begin{aligned} \Delta \cdot \Delta x & =\frac{h}{4 \pi m} \\ \Delta v \cdot \Delta x & =\frac{6.626 \times 10^{-34} \mathrm{kgm}^2 \mathrm{~s}^{-1}}{4 \times 3.14 \times 10^{-6} \mathrm{~kg}} \\ & =0.52 \times 10^{-28} \mathrm{~m}^2 \mathrm{~s}^{-1} \end{aligned} \end{aligned}$$
The value of $\Delta v \cdot \Delta x$ obtained is extremely small and is insignificant. Therefore, for milligram-sized or heavier objects, the associated uncertainties are hardly of any real consequence.
Hydrogen atom has only one electron. So, mutual repulsion between electrons is absent. However, in multielectron atoms mutual repulsion between the electrons is significant. How does this affect the energy of an electron in the orbitals of the same principal quantum number in multielectron atoms?
In hydrogen atom, the energy of an electron is determined by the value of $n$ and in multielectron atom, it is determined by $n+l$. Hence, for a given principal quantum, number electrons of $s, p, d$ and $f$-orbitals have different energy (for $s, p, d$ and $f, l=0,1,2$ and 3 respectively).
Match the following species with their corresponding ground state electric configuration.
| Atom / Ion | Electronic configuration | ||
|---|---|---|---|
| A. | Cu | 1. | $$ 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{10} $$ |
| B. | Cu$$^{2+}$$ | 2. | $$ 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{10} 4s^2 $$ |
| C. | Zn$$^{2+}$$ | 3. | $$ 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{10} 4s^1 $$ |
| D. | Cr$$^{3+}$$ | 4. | $$ 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{9} $$ |
| 5. | $$ 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{3} $$ |
A. $\rightarrow(3)$
B. $\rightarrow(4)$
C. $\rightarrow(1)$
D. $\rightarrow(5)$
A. $\mathrm{Cu}(\mathrm{Z}=29) \quad: \quad 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{10} 4 s^1$
B. $\mathrm{Cu}^{2+}(Z=29) \quad: \quad 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^9$
C. $Z n^{2+}(Z=30) \quad: \quad 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^{10}$
D. $\mathrm{Cr}^{3+}(\mathrm{Z}=24) \quad: \quad 1 s^2 2 s^2 2 p^6 3 s^2 3 p^6 3 d^3$