For the hydrogen atom where Rh=2.18*10^-18 J, the wavelength of the transition from the ground state to the n=3 state is_____?
First I don't think RH = 2.180E-18 J.
RH = 1.09737E7
1/wavelength = 1.09737E7(1/1 - 1/9) and solve for wavelength in meters.
If you want to use that 2.18E-18 J number, that can be done this way.
delta E = 2.180E-18J x (1/1 - 1/9)
Then E = hc/wavelength and solve for wavelength.
To find the wavelength of the transition from the ground state to the n=3 state in a hydrogen atom, we can use the Rydberg formula:
1/λ = Rh * (1/n1^2 - 1/n2^2)
Where:
- λ is the wavelength of the transition
- Rh is the Rydberg constant (2.18*10^-18 J)
- n1 is the initial state (ground state, n1=1)
- n2 is the final state (n=3)
Let's substitute the values into the formula and solve for λ:
1/λ = (2.18*10^-18 J) * (1/1^2 - 1/3^2)
1/λ = (2.18*10^-18 J) * (1 - 1/9)
1/λ = (2.18*10^-18 J) * (8/9)
1/λ = 1.956*10^-18 J
Taking the reciprocal of both sides:
λ = 5.104*10^17 m
Therefore, the wavelength of the transition from the ground state to the n=3 state in a hydrogen atom is approximately 5.104*10^17 meters.
To find the wavelength of the transition from the ground state to the n=3 state in a hydrogen atom, we can use the Rydberg formula:
1/λ = Rh * (1/n₁² - 1/n₂²),
where Rh is the Rydberg constant (2.18 x 10^(-18) J), n₁ is the initial energy level (ground state, n=1), and n₂ is the final energy level (n=3).
Substituting the values into the formula:
1/λ = (2.18 x 10^(-18) J) * (1/1² - 1/3²)
Calculating, we have:
1/λ = (2.18 x 10^(-18) J) * (1 - 1/9)
Simplifying:
1/λ = (2.18 x 10^(-18) J) * (8/9)
Now, we can find the inverse of λ by multiplying both sides by λ:
1 = (2.18 x 10^(-18) J) * (8/9) * λ
Multiplying and rearranging, we find:
λ = 9/(2.18 x 10^(-18) J) * (8/9)
Simplifying, we get:
λ = 8/(2.18 x 10^(-18) J)
Calculating the value of λ yields:
λ ≈ 3.67 x 10^(-7) meters
Therefore, the wavelength of the transition from the ground state to the n=3 state in the hydrogen atom is approximately 3.67 x 10^(-7) meters.