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Question

The radius of which of the following orbits is the same as that of the first Bohr's orbit of hydrogen atom?

A
He+ (n=2)
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B
Li2+ (n=2)
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C
Li2+ (n=3)
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D
Be3+ (n=2)
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Solution

The correct option is D Be3+ (n=2)
Bohr's radius for nth orbit, (rn)=0.529[n2Z]A
where n=Energy level, Z=Atomic number

For 1st Bohr orbit of hydrogen atom, n=1 and Z=1
Radius of H atom rH=0.529 A

For He+ ion: n=2, Z=2
rHe+=0.529[222]=2rH

For Li2+ ion: n=2, Z=3
rLi2+=0.529[223]=43rH

For Li2+ ion: n=3, Z=3
rLi2+=0.529[323]=3rH

For Be3+ ion: n=2, Z=4
rBe3+=0.529[224]=rH

Be3+ (n = 2) has the same radius as that of the 1st Bohr’s orbit of hydrogen atom.

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