Question

Which of the following is true?

• A. According to Pauli’s exclusion principle, no two electrons in an atom can have the same values of quantum numbers $n,l$ and $m$.
• B. The total energy of an electron in an orbital is half of its potential energy.
• C. The speed of an electron in an orbital increases with increase of quantum number $n$.
• D. The energy of an electron in an orbital decreases with increase of its quantum number $n$.

Answer 1

Answer: (B)

(a) False. The correct statement is as under: No two electrons in an atom can have the same value of all four quantum numbers $n,l,m,$ and $m_2$ (b) True.
The expressions are
$PE=\frac{Z{e}^2}{\left(4\pi {\epsilon }_0\right)r}$
$E=KE+PE$
$=\frac{1}{2}\frac{Z{e}^2}{2\left(4\pi {\epsilon }_0\right)r}-\frac{Z{e}^2}{\left(4\pi {\epsilon }_0\right)r}$
$=-\frac{1}{2}\frac{Z{e}^2}{\left(4\pi {\epsilon }_0\right)r}$
$\left(c\right)$ False. The expression of velocity is $v=\frac{1}{n}\left(constant\right)$
$\left(d\right)$ False. The expression of energy is $E=-\frac{1}{n^2}\left(constant\right)$