Question

An atom has x energy levels; then the total number of lines in the emission spectrum will be:

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

Answer 1

The correct option is D $1+2+3+....+(x-1)$

For x energy levels, the number of transitions is equal to $1+2+3+.....+(x-1)$. For example for $3$ energy levels, transitions also $1+2=3.(2=3-1)$. Thus correct answer is option D.