An atom has x energy level, then total no. of lines in its spectrum are:-

Question

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

B. 1+2+3......(x²)

C. 1+2+3......(×-1)

D. (×+1)(×+2)(×+4)

Answer 1

The correct answer will be option (C) i.e 1+2+3......(×-1)

Explanation:

Thus the number of lines emitted from nth energy level

= 1 + 2 + 3 +………… n – 1 = ∑(n – 1)

∑n =  n(n+1)/2      

Thus, ∑ (n – 1) = ( n-1) (n-1+1)/2  = (n-1) (n)/2 

Number of spectral lines that appear in spectrum when an electron jumps from nth energy level = n (n-1)/2