The transition energy for an absorption line in the electromagnetic spectrum is the energy difference between two quantum states of an atom or molecule involved in the absorption process. It corresponds to the specific wavelength or frequency of light absorbed when an electron transitions from a lower energy level to a higher one. This energy can be calculated using the equation ( E = h \nu ) or ( E = \frac{hc}{\lambda} ), where ( E ) is the transition energy, ( h ) is Planck's constant, ( \nu ) is the frequency, ( c ) is the speed of light, and ( \lambda ) is the wavelength. Each element or molecule has unique absorption lines characteristic of its electronic structure.
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The absorption line at 460 nm corresponds to a transition energy calculated using the formula ( E = \frac{hc}{\lambda} ), where ( h ) is Planck's constant (approximately ( 6.626 \times 10^{-34} ) J·s), ( c ) is the speed of light (about ( 3.00 \times 10^8 ) m/s), and ( \lambda ) is the wavelength in meters. Converting 460 nm to meters gives ( 460 \times 10^{-9} ) m. Plugging in these values, the transition energy is approximately 4.3 eV.
Transition B produces light with half the wavelength of Transition A, so the wavelength is 200 nm. This is due to the inverse relationship between energy and wavelength in the electromagnetic spectrum.
To find the approximate wavelength of the 3T1 to 3T2 transition, we can use the formula ( \lambda = \frac{1}{\nu} ), where ( \nu ) is the energy in wavenumbers (cm^-1). The energy difference for the transition can be approximated as ( \Delta E \approx \Delta_o ) for this case, which is 29040 cm^-1. Converting this to wavelength, we have: [ \lambda = \frac{1}{29040 , \text{cm}^{-1}} \times 10^7 , \text{nm/cm} \approx 344.3 , \text{nm}. ] Thus, the approximate wavelength of the 3T1 to 3T2 transition is around 344 nm.
The wavelength of visible absorption typically ranges from about 380 nanometers (nm) to 750 nm. This range corresponds to the visible spectrum, which includes violet (around 380-450 nm), blue (450-495 nm), green (495-570 nm), yellow (570-590 nm), orange (590-620 nm), and red (620-750 nm) light. Different substances absorb specific wavelengths within this range, which is why they appear in various colors.
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The second longest wavelength in the absorption spectrum of hydrogen corresponds to the transition from the n=2 to n=4 energy levels. This transition produces a spectral line known as the H-alpha line, which falls in the red part of the visible spectrum at a wavelength of 656.3 nm.
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The element that emits a spectral line at 768 nm is hydrogen. The 768 nm spectral line corresponds to the transition of an electron from the 5th energy level to the 2nd energy level in a hydrogen atom.
The absorption line at 460 nm corresponds to a transition energy calculated using the formula ( E = \frac{hc}{\lambda} ), where ( h ) is Planck's constant (approximately ( 6.626 \times 10^{-34} ) J·s), ( c ) is the speed of light (about ( 3.00 \times 10^8 ) m/s), and ( \lambda ) is the wavelength in meters. Converting 460 nm to meters gives ( 460 \times 10^{-9} ) m. Plugging in these values, the transition energy is approximately 4.3 eV.
Transition B produces light with half the wavelength of Transition A, so the wavelength is 200 nm. This is due to the inverse relationship between energy and wavelength in the electromagnetic spectrum.
The wavelength of the hydrogen atom in the 2nd line of the Balmer series is approximately 486 nm. This corresponds to the transition of an electron from the third energy level to the second energy level in the hydrogen atom.
The transition from energy level 4 to energy level 2 occurs when a hydrogen atom emits light of 486 nm wavelength. This transition represents the movement of an electron from a higher energy level (n=4) to a lower energy level (n=2), releasing energy in the form of light.
The shortest wavelength radiation in the Balmer series is the transition from the n=3 energy level to the n=2 energy level, which corresponds to the Balmer alpha line at 656.3 nm in the visible spectrum of hydrogen.
To find the approximate wavelength of the 3T1 to 3T2 transition, we can use the formula ( \lambda = \frac{1}{\nu} ), where ( \nu ) is the energy in wavenumbers (cm^-1). The energy difference for the transition can be approximated as ( \Delta E \approx \Delta_o ) for this case, which is 29040 cm^-1. Converting this to wavelength, we have: [ \lambda = \frac{1}{29040 , \text{cm}^{-1}} \times 10^7 , \text{nm/cm} \approx 344.3 , \text{nm}. ] Thus, the approximate wavelength of the 3T1 to 3T2 transition is around 344 nm.
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