Question

In a sample of hydrogen atoms, electrons are de-excited from the $7^{th}$ shell. The number of lines emitted which are not in visible region are:

• A. 5
• B. 15
• C. 16
• D. 10

Answer 1

The correct option is C 16

We get 6 lines starting from the $7^{th}$ shell which are $7\to 6$, $7\to 5$, $7\to 4$, $7\to 3$, $7\to 2$, $7\to 1$. Similarly, the total numer of lines starting from the $6^{th}$ shell will be 5 and accordingly 4, 3, 2, 1 for $5^{th}$, $4^{th}$, $3^{rd}$ and $2^{nd}$ shell respectively. So the emission spectrum contains total of $6+5+4+3+2+1=21$ lines. A simple formula would be $n(n-1))/2$ where n = 7.
The lines which are in the visible region are $7\to 2$, $6\to 2$, $5\to 2$, $4\to 2$, $3\to 2$.
Out of these, the number of lines which are not in the visible region are $21-5=16$.