For a helium ion He⁺ (nuclear charge $Z = 2$ ), find the radius of the third Bohr orbit ( $n = 3$ ). Use the Bohr radius $a_{0} = 0.529, \overset{˚}{A}$ .

medium 3 marks Class 12 · Physics · Atoms

Answer

2.38 Å

The correct answer is 2.38 Å — Round to two decimal places: $2.38, \overset{˚}{A}$ .

Step-by-step solution

Use the Bohr radius formula for hydrogen‑like ions: $r_{n} = \frac{n ^{2} , a _{0}}{Z}$ .
Insert the values: $r_{3} = \frac{3 ^{2} \times 0.529}{2} = \frac{9 \times 0.529}{2} = 4.761/2 = 2.3805, \overset{˚}{A}$ .
Round to two decimal places: $2.38, \overset{˚}{A}$ .

Common mistake: Forgetting to divide by

Z

or using

n

instead of

n^{2}

Concept tested: Bohr radius scaling with nuclear charge