What is the frequency of a photon resulting from the transition of n = 7 �¨ n = 1 ?
In what atom?
4.56x10^7 J
To calculate the frequency of a photon resulting from the transition of n = 7 to n = 1, we can use the Rydberg formula. The Rydberg formula gives the relationship between the energy levels of an electron in an atom and the frequency of the emitted or absorbed photon.
The Rydberg formula is given by:
1/λ = R * (1/n1² - 1/n2²)
Where:
- λ is the wavelength of the emitted or absorbed photon
- R is the Rydberg constant (approximately 1.097 * 10^7 m⁻¹)
- n1 and n2 are the initial and final energy levels of the electron respectively
To obtain the frequency, we need to convert the wavelength (λ) to frequency (ν). The relationship between wavelength and frequency is given by the equation:
c = λ * ν
Where:
- c is the speed of light (approximately 3.00 * 10^8 m/s)
- λ is the wavelength
- ν is the frequency
Let's follow these steps to calculate the frequency:
Step 1: Calculate the wavelength (λ) using the Rydberg formula.
1/λ = R * (1/n1² - 1/n2²)
For the given transition from n = 7 to n = 1:
n1 = 7 and n2 = 1
1/λ = 1.097 * 10^7 m⁻¹ * (1/7² - 1/1²)
Simplifying the equation:
1/λ = 1.097 * 10^7 m⁻¹ * (1/49 - 1)
Finding the common denominator and simplifying further:
1/λ = (1.097 * 10^7 m⁻¹ * (1 - 49)) / 49
1/λ = (-48.097 * 10^7 m⁻¹) / 49
Calculating the inverse of wavelength (λ) by taking the reciprocal of both sides:
λ = 49 / (-48.097 * 10^7 m⁻¹)
Step 2: Calculate the frequency (ν) using the equation c = λ * ν.
ν = c / λ
Substituting the values:
ν = (3.00 * 10^8 m/s) / (49 / (-48.097 * 10^7 m⁻¹))
Simplifying the expression:
ν = (3.00 * 10^8 m/s) * (-48.097 * 10^7 m⁻¹) / 49
Calculating the frequency:
ν = -3.08 * 10^15 Hz
Hence, the frequency of the photon resulting from the transition of n = 7 to n = 1 is approximately -3.08 * 10^15 Hz.