Question

Calculate the radius of the third orbit of $\mathrm{He^+}$.

• A. 52.9 pm
• B. 105.8 pm
• C. 238.1 pm
• D. 423.2 pm

Hint:

Chemistry Tip: For hydrogen-like ions, radius decreases as atomic number $Z$ increases.

Answer 1

The Correct Option is C

Step 1: For hydrogen-like species, $$ r_n=\frac{n^2}{Z}\times 52.9\text{ pm} $$

Step 2: For $\mathrm{He^+}$, $Z=2$ and $n=3$.

Step 3: Substitute: $$ r_3=\frac{3^2}{2}\times52.9 $$

Step 4: Calculate: $$ r_3=\frac{9}{2}\times52.9=238.1\text{ pm} $$ $$ \therefore \text{Correct option is (C).} $$