Answer
n = 4
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 Ground state. And, the wavelength of the absorbed photon is 97.20 nm.
So,
n1 = ground state = 1
λ = 97.20 nm
Unknowns :
The unknown quantity is the final Energy level of the electron
n2 = ?
3
Solution :
Substituting the values in the Rydberg's formula,
1/ 97.20 x 10^-9 = 1.0967 x 10^7 [1/(1)² - 1/(n2)²]
1 - (1/n2)² = 0.938
(1/n2)² = 0.062
(n2)² = 16 .... (approx)
n2 = 4 .... (approx)
Thus, the given electron will move to an energy level of n = 4.
