Calculate the frequency of electromagnetic radiation emitted by the hydrogen atom in the electron transition from n = 7 to n = 6.
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To calculate the frequency of electromagnetic radiation emitted by the hydrogen atom in the electron transition from n = 7 to n = 6, we can use the Rydberg formula.
The Rydberg formula is given by:
1/λ = R * (1/n1^2 - 1/n2^2)
Where:
- λ is the wavelength of the radiation emitted.
- R is the Rydberg constant (approximately 1.097 × 10^7 m^-1).
- n1 and n2 are the principal quantum numbers representing the initial and final states of the electron transition, respectively.
To calculate the frequency, we need to find the wavelength first. Since frequency (f) and wavelength (λ) are inversely related, we can then use the following equation to calculate the frequency:
f = c / λ
Where:
- f is the frequency.
- c is the speed of light (approximately 3.00 × 10^8 m/s).
Let's now substitute the values into the formulas to find the frequency:
1/λ = R * (1/n1^2 - 1/n2^2)
1/λ = 1.097 × 10^7 m^-1 * (1/7^2 - 1/6^2)
1/λ = 1.097 × 10^7 m^-1 * (1/49 - 1/36)
1/λ = 1.097 × 10^7 m^-1 * (0.02041 - 0.02778)
1/λ = 1.097 × 10^7 m^-1 * (-0.00737)
1/λ = -8.07989 × 10^4 m^-1
λ = -1/(-8.07989 × 10^4 m^-1)
λ = -1.236 × 10^-5 m (Note: The negative sign indicates that it's an emitted radiation)
Now, we can calculate the frequency using the equation:
f = c / λ
f = 3.00 × 10^8 m/s / (-1.236 × 10^-5 m)
f = -2.43 × 10^13 Hz (Note: The negative sign indicates that it's an emitted radiation)
Therefore, the frequency of electromagnetic radiation emitted by the hydrogen atom in the electron transition from n = 7 to n = 6 is approximately 2.43 × 10^13 Hz.