MCQ
The ground state energy of hydrogen atom is $-13.6 eV$. Consider an electronic state $\Psi$ of $He ^{-}$whose energy, azimuthal quantum number and magnetic quantum number are $-3.4 eV , 2$ and $0$ respectively. Which of the following statement($s$) is(are) true for the state $\Psi$ ?

$(1)$ It has $2$ angular nodes

$(2)$ It has $3$ radial nodes

$(3)$ It is a 4d state

$(4)$ The nuclear charge experienced by the electron in this state is less than $2 e$, where $e$ is the magnitude of the electronic charge.

  • $1,3$
  • B
    $1,4$
  • C
    $1,2$
  • D
    $1,2,3$

Answer

Correct option: A.
$1,3$
a
$\#-3.4=\frac{-13.6 \times 4}{n^2}$

$n =4$

$\# \ell=2$

$\# m =0$

Angular nodes $=\ell=2$

Radial nodes $=( n -\ell-1)=1$

$n\ell=4 d$ state

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