The radius of the first Bohr orbit of the H atom is r. Then, the radius of the first orbit of Li 2+ will be

Question

The radius of the first Bohr orbit of the H atom is r. Then, the radius of the first orbit of Li 2+ will be (A)  (r/9)  (B)  (r/3)  (C) 3r (D) 9r

Tardigrade Admin · Accepted Answer

Formula for radius of H-like species, rn=0.529 × (n2/Z) mathringA where, 0.529 mathringA is the Bohr radius of H-atom n= principle quantum number, Z= atomic number So, rn=(r/3)(∵ n=1, Z=3. for .Li 2+)

Q. The radius of the first Bohr orbit of the $H$ atom is $r$ . Then, the radius of the first orbit of $L i^{2 +}$ will be

$\frac{r}{9}$

$\frac{r}{3}$

$3 r$

$9 r$

Formula for radius of H-like species,
$r_{n} = 0.529 \times \frac{n ^{2}}{Z} \overset{˚}{A}$
where, $0.529 \overset{˚}{A}$ is the Bohr radius of H-atom
$n =$ principle quantum number,
$Z =$ atomic number
So, $r_{n} = \frac{r}{3} (∵ n = 1, Z = 3$ for $L i^{2 +})$

Q. The radius of the first Bohr orbit of the H atom is r. Then, the radius of the first orbit of Li2+ will be

9r​

3r​

3r

9r