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AIIMS 2014

Exam: AIIMS
Year: 2014
Subject: Physics
Chapter: Atomic Physics

AIIMS 2014 · Physics · Atomic Physics

A triply ionized beryllium (Be^ 3+ ) has the same orbital radius as...

A triply ionized beryllium

\left(\mathrm{Be}^{3+}\right)

has the same orbital radius as the ground state of hydrogen. Then the quantum state

n of \mathrm{Be}^{3+}

is

Options

A $n=1$
B $n=2$
C $n=3$
D $n=4$

Correct answer

B. $n=2$

Step-by-step solution

Radius of

n^{\text{th }}

orbit in hydrogen like atoms is

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

where

a_0

is the Bohr's radius For hydrogen atom,

Z=1 \therefore r_1=a_0 \quad(\because n=1

for ground state

)

For

\mathrm{Be}^{3+}, Z=4 \therefore r_n=\frac{a_0 n^2}{4}

According to given problem

r_1=r_n a_0=\frac{n^2 a_0}{4} n=2

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