Question

Which hydrogen like species will have the same radius of 1st Bohr's orbit of a hydrogen atom?

• A. $n=2,{Li}^{+2}$
• B. $n=2,{Be}^{+3}$
• C. $n=2,{He}^{+}$
• D. $n=3,{Li}^{+2}$

Answer 1

Answer: (B)

$n=2,{Be}^{+3}$

As we know that,

$r=r_0\frac{n^2}{Z}$

whereas,

$r_0=$ radius of $1^{st}$ Bohr's orbit of hydrogen atom $=0.529\mathring{A}$

For $r=r_0$-

$\frac{n^2}{Z}=1$

$\Rightarrow n^2=Z.....\left(1\right)$

$\because$ For $n=2,{Be}^{+3}$,

$Z=4$, which satisfies equation $\left(1\right)$.

Hence, $n=2,{Be}^{+3}$ will have the same radius of $1^{st}$ Bohr's orbit of a hydrogen atom.