Question

X\(^{a+}\) and Y\(^{b+}\) are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers \(n = 1\) and \(n = 2\) of X\(^{a+}\) is \(\lambda\). The wavelength of light absorbed during the transition between the states with principal quantum numbers \(n = 2\) and \(n = 4\) of Y\(^{b+}\) is \(9\lambda\). The lowest possible value of \((a+b)\) is _______.

Hint:

Remember the Rydberg formula for hydrogen-like species. Focus on the $Z^2$ term. When relating wavelengths, setting up a ratio of the Rydberg formulas often leads to simple relationships between atomic numbers. The charges $a$ and $b$ are always one less than the atomic number $Z$.

Answer 1

Correct Answer: 3