A hydrogen atom electron in an excited state with n = 7 drops to a lower energy state with n = 3. What is the wavelength of the light emitted in this transition
1/wavelength = R(1/3^2 - 1/7^2)
R = Rydberg constant = 1.097373E7
wavelength is in m.
To find the wavelength of the light emitted in the transition of a hydrogen atom electron, we can use the Rydberg formula. The formula is given by:
1/λ = R * (1/n1^2 - 1/n2^2)
Where:
- λ is the wavelength of light emitted
- R is the Rydberg constant, approximately 1.097 x 10^7 m^-1
- n1 and n2 are the initial and final energy levels, respectively
In this case, the initial energy level (n1) is 7 and the final energy level (n2) is 3. Plug these values into the formula:
1/λ = R * (1/7^2 - 1/3^2)
Simplifying the equation:
1/λ = R * (1/49 - 1/9)
1/λ = R * (9 - 49) / (49 * 9)
1/λ = R * -40 / 441
1/λ = -40R / 441
Now, divide both sides by -40R to solve for λ:
λ = 441 / (-40R)
Substituting the value of the Rydberg constant, we get:
λ = 441 / (-40 * 1.097 x 10^7)
λ ≈ 6.56 x 10^-7 meters
Therefore, the wavelength of the light emitted in this transition is approximately 6.56 x 10^-7 meters.
To find the wavelength of the light emitted during the transition of the hydrogen atom electron, we can use the formula for calculating the wavelength of light emitted when an electron moves between energy levels in a hydrogen atom.
The formula is:
1/λ = R * (1/n1^2 - 1/n2^2)
where λ is the wavelength of the emitted light, R is the Rydberg constant (approximately 1.097 × 10^7 m^-1), n1 is the initial energy level, and n2 is the final energy level.
In this case, the initial energy level (n1) is 7 and the final energy level (n2) is 3. Substituting these values into the formula, we get:
1/λ = 1.097 × 10^7 * (1/7^2 - 1/3^2)
Simplifying this equation gives:
1/λ = 1.097 × 10^7 * (1/49 - 1/9)
1/λ = 1.097 × 10^7 * (9/441 - 49/441)
1/λ = 1.097 × 10^7 * (-40/441)
1/λ = -40 × 10^7 / 441
1/λ = -40 × 10^7 / 441
Multiplying both sides by λ gives:
λ = 441 / (-40 × 10^7)
Calculating this value will give us the wavelength of the emitted light in meters.