Question

Hydrogen atoms are excited from ground state to the state of principal quantum number 4, then, what will be the number of spectral lines observed?

• A. 6
• B. 5
• C. 2
• D. 3
• E. 1
• F. 4

Answer 1

Answer: (A)

6

Answer 2

When hydrogen atoms are excited to a principal quantum number 'n', the total number of possible spectral lines observed during de-excitation to lower energy states is given by the formula:

$N = \frac{n(n-1)}{2}$

In this question, the principal quantum number (n) to which the hydrogen atoms are excited is 4. Substitute n = 4 into the formula:

$N = \frac{4(4-1)}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6$

Therefore, 6 spectral lines will be observed.