Answer
n=3
Work Step by Step
1
Analysis :
Rydberg's Equation is given as :
1/ λ = R [1/(n1)² - 1/(n2)²]
Where,
λ : Wavelength
R : Rydberg's Constant = 1.0967 x 10^7 / m
n1 & n2 : Positive constants corresponding to the energy levels involved.
2
Knowns :
Here, it is given that the Hydrogen atom is in it's 5th state, and the wavelength of the emitted photon is 1281 nm.
So,
n2 = 5
λ = 1281 nm = 1281 x 10^-9 m = 1.281 x 10^-6 m
Unknowns :
The unknown quantity is the final Energy level of the electron
n1 = ?
3
Solution :
Substituting the values in the Rydberg's formula,
1/ 1.281 x 10^-6 = 1.0967 x 10^7 [1/(n1)² - 1/(5)²]
1 / 14.048 = 1/(n1)² - 1/(5)²
(1/n1)² = 0.111
(n1)² = 9.09
n1 = 3 .... (approx)
Thus, the given electron will move to an energy level of n = 3.
