According to Bohr’s model, the radius of the first excited state (n = 2) of the hydrogen atom is given by $r_{n} = n^{2} a_{0}$ , where $a_{0} = 0.529 \times 1 0^{- 10}, m$ is the Bohr radius. Calculate $r_{2}$ in meters.

hard 3 marks Class 11 · Chemistry · Some Basic Concepts of Chemistry

Answer

2.116 \times 1 0^{- 10}, m

The correct answer is $2.116 \times 1 0^{- 10}, m$ — Thus $r_{2} = 2.116 \times 1 0^{- 10}, m$ .

Step-by-step solution

Write the formula for the radius of the nth orbit: $r_{n} = n^{2} a_{0}$ .
Substitute $n = 2$ to obtain $r_{2} = 2^{2} a_{0} = 4 a_{0}$ . Use the given value of $a_{0} = 0.529 \times 1 0^{- 10}, m$ .
Multiply: $4 \times 0.529 \times 1 0^{- 10}, m = 2.116 \times 1 0^{- 10}, m$ .
Thus $r_{2} = 2.116 \times 1 0^{- 10}, m$ .

Common mistake: Forgetting to square the principal quantum number

Concept tested: Atomic structure (Bohr model)