Answer:
1875 nm
Explanation:
As per the data given:
Initial orbit of electron = ni = 4
Final orbit of electron = nf = 3.
As we know that,
Speed of electromagnetic waves = c = 3 × 10^8 m/s
Planck’s constant = h = 6.63 × 10^−34 Js.
We will use Rydberg’s equation to get the wavelength or λ.
1/λ=R (1/nf^2 – 1/ni^2)
Here, R= Rydberg Constant 1.0974x10^7 m-1; λ is the wavelength; n is equal to the energy level (initial and final)
1/λ=R (1/nf^2 – 1/ni^2)
1/λ =1.0974x10^7 (1/3^2 – 1/4^2)
1/λ =1.0974x10^7 (1/9 – 1/16)
1/λ =1.0974x10^7 (0.0486)
1/λ=0.05333x 10^7
λ= 1/ 0.05333x 10^7
λ =1.875 x10^ -6m
Converting λ =1.875 x10^-6m to nanometers (nm
)
As, 1 m=10^9 nm
λ =1.875 x10^-6m x 10^9
λ =1875 nm
Note:
The value 1.0974x10^7 in the Rydberg equation comes from the Bohr equation and is equal to delta E / hc:
delta E / hc = (2.18 x 10^-18 J) / (6.626 x 10^-34 J s)(3.00 x 10^8 m/s) = 1.0967 x 10^7
Hope it helps! :)
