Question

Radius of the 2^nd orbit of He⁺ is r₀. Radius of the 4^th orbit of Be³⁺ is xr₀. Find x.

Answer 1

Given:
Radius of 2^nd orbit of He⁺ = r₀
Find radius of 4^th orbit of Be³⁺

Step 1: Bohr radius formula
r ∝ n² / Z

Step 2: For He⁺
Z = 2, n = 2
\[ r_0 = \frac{2^2}{2} = \frac{4}{2} = 2k \]

Step 3: For Be³⁺
Z = 4, n = 4
\[ r = \frac{4^2}{4} = \frac{16}{4} = 4k \]

Step 4: Ratio
\[ x = \frac{r}{r_0} = \frac{4k}{2k} = 2 \]

Final Answer: 2