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(D) The energy of stationary states in hydrogen-like atoms is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$,which is inversely proportional to $n

Vedclass · Accepted Answer

Total number of nodes for $3s$ orbital is three.

Vedclass · Answer

(D) The energy of stationary states in hydrogen-like atoms is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$,which is inversely proportional to $n^2$. Thus,option $A$ is correct.
The radius of the $n^{th}$ orbit is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$. For $H$ $(Z=1, n=1)$,$r_1 = 0.529 \ \mathring{A}$. For $He^{+}$ $(Z=2, n=1)$,$r_1 = 0.529 	imes \frac{1^2}{2} = 0.2645 \ \mathring{A}$. Since $0.2645$ is half of $0.529$,option $B$ is correct.
The angular quantum number $(l)$ determines the shape of the orbital. Thus,option $C$ is correct.
The total number of nodes in an orbital is given by $n - 1$. For the $3s$ orbital,$n = 3$,so the total number of nodes is $3 - 1 = 2$. Option $D$ states the number of nodes is $3$,which is incorrect.

$A$. Energy of ground state of $He^+$	$i$. $+6.04 \text{ eV}$
$B$. Potential energy of $I$ orbit of $H$ atom	$ii$. $-27.2 \text{ eV}$
$C$. Kinetic energy of $II$ excited state of $He^+$	$iii$. $8.72 \times 10^{-18} \text{ J}$
$D$. Ionization potential of $He^+$	$iv$. $-54.4 \text{ eV}$

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

The statement that is $NOT$ correct is:

Similar Questions

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

The shape of the probability distribution curve for the $2s$ orbital is .........

Which one is the wrong statement?

For the given electronic transitions,which of the following statements is correct?

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