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Question: The radius of n<sup>th</sup> orbit \(r_{n}\) in terms of Bohr radius \(\left( a_{0} \right)\) for a ...

The radius of nth orbit rnr_{n} in terms of Bohr radius (a0)\left( a_{0} \right) for a hydrogen atom is given by the relation

A

na0na_{0}

B

n a0\sqrt{n}\ a_{0}

C

n2a0n^{2}a_{0}

D

n3a0n^{3}a_{0}

Answer

n2a0n^{2}a_{0}

Explanation

Solution

The radius of nth orbit

rn=n2h24πε0me2r_{n} = n^{2}\frac{h^{2}4\pi\varepsilon_{0}}{me^{2}}

Where h24πε0me2=a0\frac{h^{2}4\pi\varepsilon_{0}}{me^{2}} = a_{0} (Bohr radius)

Hence, rn=n2a0r_{n} = n^{2}a_{0}