Show that the shortest wavelength lines in Lyman,Balmer and Paschen series have their wavelength in the ratio 1:4:9.

Explanation

To show that the shortest wavelength lines in the Lyman, Balmer, and Paschen series have their wavelengths in the ratio 1:4:9, we will follow these steps:

### Step 1: Understand the Series
The Lyman series corresponds to transitions where the electron falls to the first energy level (n=1). The Balmer series corresponds to transitions to the second energy level (n=2), and the Paschen series corresponds to transitions to the third energy level (n=3).

### Step 2: Calculate the Shortest Wavelength for the Lyman Series
For the Lyman series, the shortest wavelength occurs when the electron transitions from n=∞ to n=1. The formula for the wavelength (λ) is given by:

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