The radius of the hydrogen atom in its ground state is 0.53 mathringA. The radius of He+ ion in second excited state is

Question

The radius of the hydrogen atom in its ground state is 0.53 mathringA. The radius of He+ ion in second excited state is (A) 3.4 mathringA (B) 4.4 mathringA (C) 2.4 mathringA (D) 1.4 mathringA

Tardigrade Admin · Accepted Answer

The radius of nth orbit of hydrogen like atoms is rn =( n2 a0/Z) where a0 = 0.53 mathringA For He+ ion, Z = 2 For second excited state n = 3 ∴ (r3)He+ =( (3)2×0.53 mathringA/(2)) = 2.4 mathringA

Q. The radius of the hydrogen atom in its ground state is $0.53 \overset{˚}{A}$ . The radius of $H e^{+}$ ion in second excited state is

$3.4 \overset{˚}{A}$

$4.4 \overset{˚}{A}$

$2.4 \overset{˚}{A}$

$1.4 \overset{˚}{A}$

The radius of $n^{t h}$ orbit of hydrogen like atoms is
$r_{n} = \frac{n ^{2} a _{0}}{Z}$ where $a_{0} = 0.53 \overset{˚}{A}$
For $H e^{+}$ ion, $Z = 2$
For second excited state $n = 3$
$∴ (r_{3})_{H e^{+}} = \frac{( 3 ) ^{2} \times 0.53 A ˚}{( 2 )}$
$= 2.4 \overset{˚}{A}$

Q. The radius of the hydrogen atom in its ground state is 0.53A˚. The radius of He+ ion in second excited state is

3.4A˚

4.4A˚

2.4A˚

1.4A˚