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Structure of Atom question

2020 · 8 Jan · Shift 2 · Q16

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Structure of Atom
2020 · 8 Jan · Shift 2 · Q16

Structure of Atom question

2020 · 8 Jan · Shift 2 · Q16

JEE MainChemistryStructure of AtomMCQ+4 / −1

The radius of the second Bohr orbit, in terms of the Bohr radius, a0, in

Li^{2+}

is :

A
${{2{a_0}} \over 9}$
B
${{2{a_0}} \over 3}$
C
${{4{a_0}} \over 9}$
D
${{4{a_0}} \over 3}$

View written solutionFree

Correct answer: D

For a hydrogen-like species, the radius of the $n$ th Bohr orbit is given by

$r_n = \frac{n^2 a_0}{Z}$

where:

$n$ = orbit number
$a_0$ = Bohr radius
$Z$ = atomic number

For $Li^{2+}$ :

Lithium has atomic number $Z=3$
Second Bohr orbit means $n=2$

So,

$r_2 = \frac{(2)^2 a_0}{3} = \frac{4a_0}{3}$

Therefore, the radius of the second Bohr orbit is

$\boxed{\frac{4a_0}{3}}$

Comparing with the options:

A: $\frac{2a_0}{9}$
B: $\frac{2a_0}{3}$
C: $\frac{4a_0}{9}$
D: $\frac{4a_0}{3}$

Hence, the correct option is D.

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