Question

in H atom if e- moves from nth orbit to 1st orbit by transiston in multi steps if there are total no. of lines in spectrum are 10 then find out the value of n?

Answer 1

If an electron jumps from n₂ to n₁ then the possible number of spectral lines is given by the expression (n₂ - n₁)( n₂ - n₁ + 1) × 1/2

given the value of n₁ = 1 and n₂ = n the total number of spectral lines = 10

substituting the above values in the above explanation we get

(n - 1)( n - 1 + 1 ) × 1/2 = 10

(n - 1)(n) = 20

(n)² - n - 20 = 0

(n)² - 5n + 4n - 20 = 0

n( n - 5) + 4(n - 5) = 0

n = 5 and n = -4

n = -4 cannot be correct value as the number of spectral lines is positive integer

⇒ n = 5

so the electron moved from 5th orbit to 1st orbit to produce a total number of 10 spectral lines.