The ground state energy of hydrogen atom is -13.6 eV . Consider an electronic state $\Psi$ of $\math

Question

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

Professor PC Thomas Classes · Answer

$(\mathrm{a}, \mathrm{d}): E_{\mathrm{He}^{+}}=-13.6 	imes \frac{(2)^{2}}{n^{2}}$;\ $-3.4=-13.6 	imes \frac{4}{n^{2}}$\ $n^{2}=16$, so $n=4$\ Quantum numbers are $n=4, l=2, m=0$ So, subshell is $4 d$.\ Angular node $=l=2$\ Radial node $=(n-l-1)=(4-2-1)=1$