Question

Arrange the following set of quantum numbers having highest energy of an electron.

($\mathrm{p}$) $\mathrm{n}=4,\mathrm{l}=1,\mathrm{m}=+1,\mathrm{s}=+1/2$

($\mathrm{q}$) $\mathrm{n}=4,\mathrm{l}=2,\mathrm{m}=-1,\mathrm{s}=-1/2$

($\mathrm{r}$) $\mathrm{n}=3,\mathrm{l}=2,\mathrm{m}=0,\mathrm{s}=+1/2$

($\mathrm{s}$) $\mathrm{n}=3,\mathrm{l}=1,\mathrm{m}=+1,\mathrm{s}=-1/2$

• A. ($\mathrm{q}$) > ($\mathrm{r}$) > ($\mathrm{p}$) > ($\mathrm{s}$)
• B. ($\mathrm{q}$) > ($\mathrm{p}$) > ($\mathrm{r}$) >($\mathrm{s}$)
• C. ($\mathrm{s}$) > ($\mathrm{p}$) > ($\mathrm{r}$) > ($\mathrm{q}$)
• D. ($\mathrm{s}$) > ($\mathrm{r}$) > ($\mathrm{p}$) > ($\mathrm{q}$)

Answer 1

The correct option is B

($\mathrm{q}$) > ($\mathrm{p}$) > ($\mathrm{r}$) >($\mathrm{s}$)

Step 1:

1. Higher the value of $\mathrm{n}$ (principle quantum number), higher is the energy of the electron.
2. When the value of $\mathrm{n}$ becomes equal from two set of values then higher the value of $(\mathrm{n}+\mathrm{l})$, higher is the energy of the electron.

Step 2:

On the basis of point 1 we can say that energy of electron in case of ($\mathrm{p}$) and ($\mathrm{q}$) is greater than ($\mathrm{r}$) and ($\mathrm{s}$). The value of $\mathrm{n}$ for ($\mathrm{p}$) and ($\mathrm{q}$) is $4$ and the value of $\mathrm{n}$ for ($\mathrm{r}$) and ($\mathrm{s}$) which is $3$.

So, we can write energy order as ($\mathrm{p}$), ($\mathrm{q}$) $>$ ($\mathrm{r}$), ($\mathrm{s}$)

Step 3:

Now, value of $(\mathrm{n}+\mathrm{l})$ for ($\mathrm{p}$) is $=4+1$

$\mathrm{n}+\mathrm{l}=5$

Now, value of $(\mathrm{n}+\mathrm{l})$ for ($\mathrm{q}$) is $=4+2$

$\mathrm{n}+\mathrm{l}=6$

We can write energy order as ($\mathrm{q}$) > ($\mathrm{p}$)

Step 4:

Now, value of $(\mathrm{n}+\mathrm{l})$ for ($\mathrm{r}$) is $=3+2$

$\mathrm{n}+\mathrm{l}=5$

Now, value of $(\mathrm{n}+\mathrm{l})$ for ($\mathrm{s}$) is $=3+1$

$\mathrm{n}+\mathrm{l}=4$

We can write energy order as ($\mathrm{r}$) $>$ ($\mathrm{s}$)

Final energy order can be written as ($\mathrm{q}$) > ($\mathrm{p}$) > ($\mathrm{r}$) > ($\mathrm{s}$)

Hence, option B is the correct answer.