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(D) The wave function for the $1s$ orbital of a hydrogen atom is given by $\Psi_{1s} = \frac{1}{\sqrt{\pi a_0^3}} e^{-r/a_0}$.$A.$ The probability den

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The total energy of the electron is maximum when it is at a distance $a_0$ from the nucleus

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(D) The wave function for the $1s$ orbital of a hydrogen atom is given by $\Psi_{1s} = \frac{1}{\sqrt{\pi a_0^3}} e^{-r/a_0}$.$A.$ The probability density $\Psi^2$ is proportional to $e^{-2r/a_0}$. At $r = 0$ (nucleus),$\Psi^2$ is maximum. This statement is correct.$B.$ The electron has a non-zero probability of being found at any distance $r$ from the nucleus,including $2a_0$. This statement is correct.$C.$ The $1s$ orbital has no angular dependence,making it spherically symmetrical. This statement is correct.$D.$ The total energy of an electron in a hydrogen atom is given by $E_n = -\frac{13.6 \ eV}{n^2}$. This energy is constant for a given orbital and does not depend on the distance $r$ from the nucleus. The energy is maximum (zero) at $r = \infty$. Therefore,this statement is incorrect.

Column-$I$	Column-$II$
$(1)$ Photon	$(A)$ Value of $4$ for $N$ shell
$(2)$ Electron	$(B)$ Probability density
$(3)$ $\psi^2$	$(C)$ Always $+$ value
$(4)$ Principal quantum number $(n)$	$(D)$ Represents wavelength and momentum

Which one of the following about an electron occupying the $1s$ orbital in a hydrogen atom is incorrect? (Bohr's radius is represented by $a_0$)

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Match the following columns:

Column-$I$ Column-$II$

$(1)$ Photon $(A)$ Value of $4$ for $N$ shell

$(2)$ Electron $(B)$ Probability density

$(3)$ $\psi^2$ $(C)$ Always $+$ value

$(4)$ Principal quantum number $(n)$ $(D)$ Represents wavelength and momentum

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