The wavelength of emitted light is calculated as (a) is 122 nm, (b) is 103 nm, (c) is 486 nm, and for (d) is 434 nm.
<h3>What is Rydberg´s equation?</h3>
The Rydberg formula is mathematical formula for evaluating wavelength of light emitted by electron moving between the energy levels of an atom.
We can find out the wavelength emitted in the hydrogen atom electron transitions using Rydberg´s equation.
using, 1/λ = Rh x ( 1/n₁² - 1/n₂² )
where λ is wavelength;
Rh is Rydberg´s constant 1.097 x 10⁷/m;
n₁, n₂ are the principal quantum numbers
a.) Given, n₁ = 1 and n₂ = 2
1/λ = 1.097 x 10⁷/m x ( 1/1² - 1/2² ) = 8.228 x 10⁶ / m
Taking inverse on both sides :
λ = 1 /8.228 x 10⁶ /m = 122 nm
b.) Given, n₁ = 1 and n₂ = 3
1/λ = 1.097 x 10⁷/m x ( 1/1² - 1/3² ) = 9.751 x 10⁶ / m
λ = 1 /9.751 x 10⁶ /m = 103 nm
c.) Given, n₁ = 2 , n₂ = 4
1/λ = 1.097 x 10⁷/m x ( 1/2² - 1/4² ) = 2.057 x 10⁶ / m
λ = 1 /2.057 x 10⁶ /m = 486 nm
d.) Given, n₁ = 2 , n₂ = 5
1/λ = 1.097 x 10⁷/m x ( 1/2² - 1/5² ) = 2.304 x 10⁶ / m
λ = 1 /2.304 x 10⁶ /m = 434 nm
To know more about Rydberg´s equation, refer
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Note: The question on portal is incomplete. Here is the complete question.
Question: Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each of the following transitions.
a. n = 2 --> n = 1 ?
b. n = 3 --> n = 1 ?
c. n = 4 --> n = 2 ?
d. n = 5 --> n = 2 ?
