Calculate the wave number for the longest wavelength transition in the Balmer series of atomic hydrogen . `( R_(H) = 109677 cm^(-1)).`

Explanation

To calculate the wave number for the longest wavelength transition in the Balmer series of atomic hydrogen, we can follow these steps:

### Step 1: Identify the Transition
In the Balmer series, the transitions occur from a higher energy level (n2) to the second energy level (n1 = 2). The longest wavelength corresponds to the smallest energy transition, which is from n2 = 3 to n1 = 2.

### Step 2: Write the Formula for Wave Number
The wave number (ṽ) can be calculated using the formula:
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