Question

An atom has x energy level, then total number of lines in its spectrum are :

• A. 1 + 2 + 3 ...................(x + 1)
• B. 1 + 2 + 3 ..........$\left(x^2\right)$
• C. 1 + 2 + 3..................(x - 1)
• D. (x + 1) (x + 2) (x + 4)

Answer 1

Answer: (C)

1 + 2 + 3..................(x - 1)

An atom has x energy level then total number of lines in its spectrum are 1 + 2 + 3..................(x - 1).

For example:

When an atom has 5 energy levels, the total number of lines in its spectrum will be $1+2+3+4=10$.
These lines corresponds to following transitions.
$5\to 1$
$4\to 1$
$3\to 1$
$2\to 1$
$5\to 2$
$4\to 2$
$3\to 2$
$5\to 3$
$4\to 3$
$5\to 4$