The species having identical radii according to the Bohr's theory are:
A. $H$ (first orbit)
B. $He^+$ (first orbit)
C. $He^+$ (Second orbit)
D. $Li^{2+}$ (first orbit)
E. $Be^{3+}$ (Second orbit)
Choose the correct answer from the options given below:

Question

The species having identical radii according to the Bohr's theory are:
A.

H

(first orbit)
B.

He^+

(first orbit)
C.

He^+

(Second orbit)
D.

Li^{2+}

(first orbit)
E.

Be^{3+}

(Second orbit)
Choose the correct answer from the options given below:

Quantrex Academy · Accepted Answer

Correct answer: B. A and E Only

According to Bohr's theory, the radius of the

n

-th orbit of a hydrogen-like species is given by

r_n = 0.529 \times \dfrac{n^2}{Z} \text{ \AA}

.

For

H

(first orbit),

n = 1

,

Z = 1 \Rightarrow r = 0.529 \times \dfrac{1^2}{1} = 0.529 \text{ \AA}

.

For

He^+

(first orbit),

n = 1

,

Z = 2 \Rightarrow r = 0.529 \times \dfrac{1^2}{2} = 0.2645 \text{ \AA}

.

For

He^+

(second orbit),

n = 2

,

Z = 2 \Rightarrow r = 0.529 \times \dfrac{2^2}{2} = 1.058 \text{ \AA}

.

For

Li^{2+}

(first orbit),

n = 1

,

Z = 3 \Rightarrow r = 0.529 \times \dfrac{1^2}{3} = 0.176 \text{ \AA}

.

For

Be^{3+}

(second orbit),

n = 2

,

Z = 4 \Rightarrow r = 0.529 \times \dfrac{2^2}{4} = 0.529 \text{ \AA}

.

The radii of

H

(first orbit)

and Be^{3+}

(second orbit) are identical. Therefore, species A and E have identical radii.

Answer: A and E Only

The species having identical radii according to the Bohr's theory...