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Hydrogen atoms are excited from ground state to the state of principal quantum number 4. Then the number of spectral lines observed will be ______.

Asked in GUJCET 2016 · Number of spectral lines

• (1) 3
• (2) 6
• (3) 5
• (4) 2

Step-by-step solution

Why the other options are wrong

• (1) 3 counts only the jumps that start from n=4 (4→3, 4→2, 4→1) and misses 3→2, 3→1 and 2→1 from the levels passed on the way down.
• (3) 5 is not a count (n(n-1))/2 can give; that expression runs 1,3,6,10, so no starting level yields exactly five lines.
• (4) 2 is not a count (n(n-1))/2 can give either; the two smallest counts are 1 (from n=2) and 3 (from n=3).

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