First slide

Classical atomic models

Question

The ground state energy of hydrogen atom is – 13.6 eV. Consider an electronic state Y 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 from the state Y?

Moderate

A

It is a 4d state
B

It has 3 radial nodes
C

It has 2 angular nodes
D

The nuclear charge experienced by the electron in this state is less than two electron, where electron is the magnitude of the electronic charge

Solution

$E = - 13.6 \times \frac{2^{2}}{n^{2}} = - 3.4$
$13.6 \times \frac{2^{2}}{n^{2}} = 3.4$
$n^{2} = 4^{2} \Rightarrow n = 4$
Wave function corresponds to $ψ_{4, 2, 0}$ $4 d_{z^{2}}$ - orbital which has only one radial nodes and two angular nodes. It experiences nuclear change of 2 electron units.

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