Example 5 Find the relation for the short -wavelength boundary of the Lyman series

The correct answer is: 1/λ = R_H * (1/1^2 - 1/2^2)<br /><br />Explanation: The Lyman series corresponds to transitions to the n=1 energy level in hydrogen. The short-wavelength boundary of the Lyman series is determined by the transition from the n=2 energy level to the n=1 energy level. Using the Rydberg formula, the wavelength of the transition can be calculated as:<br /><br />1/λ = R_H * (1/1^2 - 1/2^2)<br /><br />where λ is the wavelength, R_H is the Rydberg constant, and n is the principal quantum number.