Which of the following statements is correct | vedclass

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(C) The radius of an orbit is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
For $r_{2H}$,$n=2, Z=1 \implies r_{2H} = 0.529 	imes 4 = 2

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Total Energy $E_{1H} < E_{2H} < E_{3H}$

Vedclass · Answer

(C) The radius of an orbit is given by $r_n = 0.529 imes \frac{n^2}{Z} \ \mathring{A}$. For $r_{2H}$,$n=2, Z=1 \implies r_{2H} = 0.529 imes 4 = 2.116 \ \mathring{A}$. For $r_{1He^{+}}$,$n=1, Z=2 \implies r_{1He^{+}} = 0.529 imes \frac{1}{2} = 0.2645 \ \mathring{A}$. For $r_{1H}$,$n=1, Z=1 \implies r_{1H} = 0.529 \ \mathring{A}$. Thus,$r_{2H} > r_{1H} > r_{1He^{+}}$,so option $A$ is incorrect. Ionisation energy is given by $I.E. = 13.6 imes \frac{Z^2}{n^2} \ ext{eV}$. $I.E._{H} (Z=1, n=1) = 13.6 \ ext{eV}$. $I.E._{He^{+}} (Z=2, n=1) = 13.6 imes 4 = 54.4 \ ext{eV}$. $I.E._{Li^{+2}} (Z=3, n=1) = 13.6 imes 9 = 122.4 \ ext{eV}$. Thus,$I.E._{Li^{+2}} > I.E._{He^{+}} > I.E._{H}$,so option $B$ is incorrect. Total energy is $E_n = -13.6 imes \frac{Z^2}{n^2} \ ext{eV}$. $E_{1H} = -13.6 \ ext{eV}$,$E_{2H} = -3.4 \ ext{eV}$,$E_{3H} = -1.51 \ ext{eV}$. Since $-13.6 < -3.4 < -1.51$,$E_{1H} < E_{2H} < E_{3H}$ is correct. Option $C$ is correct.

Which of the following statements is correct regarding the properties of hydrogen-like species?

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