Question

Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6Å$. The radius of the third Bohr orbit of $He^+$is _______ picometer. (Nearest Integer)

Answer 1

Correct Answer: 270

The radius of the \(n\)-th Bohr orbit is given by: \[ r_n = r_1 \frac{n^2}{Z} \] For \(n = 3\) and \(Z = 2\): \[ r_{\text{He}^{+}} = 0.6 \times \frac{3^2}{2} = 2.7 \, \text{Å} \] Converting to picometers: \[ 2.7 \, \text{Å} = 270 \, \text{pm} \]