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The ground state energy of a 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 $2e$,where $e$ is the magnitude of the electronic charge.

Which of the following is the correct plot for the probability density $\psi^{2}(r)$ as a function of distance '$r$' of the electron from the nucleus for $2s$ orbital?

How many unpaired electrons are present in the $Ni^{2+}$ cation (atomic number $= 28$)?

Values of the four quantum numbers for the last electron in the atom are $n = 4, l = 1, m = +1$ and $s = -1/2$. Atomic number of the atom will be

The number of nodal planes in a $p_x$ orbital is:

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