What is the wavelength of the electromagnetic radiation emitted from a hydrogen atom when the electron undergoes the transition n = 5 to n = 3?((Broken Link Removed) is a spectrum
m In what region of the spectrum does the line occur?
near ultraviolet
far ultraviolet
near infrared
far infrared
visible
Both near ultraviolet and far ultraviolet are wrong I put 2.27e-7 for the answer and was wrong and then I put 2.53e-7 in it was wrong as well.
Come on. Paschen series in infared, n5 6o n3 would be closest to visible, or near infared.
But your book may define 1281.81 nm as other classifications, so check.
To calculate the wavelength of the electromagnetic radiation emitted during the transition from n = 5 to n = 3 in a hydrogen atom, we can use the Rydberg formula:
1/λ = R * (1/n₁² - 1/n₂²)
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 initial and final energy levels, respectively.
Substituting the values into the formula, we have:
1/λ = 1.097 × 10^7 * (1/5² - 1/3²)
1/λ = 1.097 × 10^7 * (1/25 - 1/9)
1/λ = 1.097 × 10^7 * (9/225 - 25/225)
1/λ = 1.097 × 10^7 * (-16/225)
Simplifying further:
1/λ = -0.0773067 × 10^7
Taking the reciprocal of both sides:
λ = -12.93 × 10^(-8) m
Since wavelength cannot be negative, we ignore the negative sign and obtain the positive value:
λ = 12.93 × 10^(-8) m
Converting to scientific notation:
λ = 1.293 × 10^(-7) m
Therefore, the wavelength of the electromagnetic radiation emitted during the transition is approximately 1.293 × 10^(-7) meters, or 129.3 nm.
In terms of the region of the spectrum, a wavelength of 1.293 × 10^(-7) meters corresponds to the near ultraviolet region.
To determine the wavelength of the electromagnetic radiation emitted during the transition of the electron in a hydrogen atom from n=5 to n=3, you can use the Rydberg formula:
1/λ = R (1/n₁² - 1/n₂²)
Where:
- λ is the wavelength of the radiation
- R is the Rydberg constant (approximately 1.097 x 10^7 m^-1)
- n₁ and n₂ are the initial and final energy levels, respectively
Plugging in the values for n₁ and n₂ into the formula, we get:
1/λ = R (1/5² - 1/3²)
1/λ = R (1/25 - 1/9)
1/λ = R (9/225 - 25/225)
1/λ = R (-16/225)
λ = -225/(16R)
To find the correct wavelength, you need to substitute the correct value for R into the formula. However, in this case, the spectrum name is provided as a hint for the region of the spectrum where this line occurs.
The given options are:
- near ultraviolet
- far ultraviolet
- near infrared
- far infrared
- visible
To determine which region of the spectrum the line occurs, you need to know the general range or approximate value for each region.
In the electromagnetic spectrum, the regions are generally defined as follows:
- Near Ultraviolet: Wavelengths ranging approximately from 10 nm to 400 nm (1 nm = 10^-9 m)
- Far Ultraviolet: Wavelengths ranging approximately from 100 nm to 10 nm
- Near Infrared: Wavelengths ranging approximately from 700 nm to 1.5 μm (1 μm = 10^-6 m)
- Far Infrared: Wavelengths ranging approximately from 1 mm to 100 μm
- Visible: Wavelengths ranging approximately from 400 nm to 700 nm
Based on the given wavelength values of 2.27e-7 and 2.53e-7 that you tried, it seems you are trying to find the wavelength in meters. However, these values are within the range of near infrared, which contradicts the given options for the correct region.
To find the correct answer, you may need to double-check the provided options or the wavelength values you used.