Wavelength, temperature in transition

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SUMMARY

This discussion focuses on three physics problems related to hydrogen atom transitions and blackbody radiation. The first problem involves calculating the wavelength of the n=1 to n=2 transition using the formula for electron energy in hydrogen atoms. The second problem applies Wien's law to determine the surface temperature of a star based on the peak intensity of blackbody radiation corresponding to the n=1 to n=2 transition. The third problem addresses the hyperfine transition of hydrogen discovered by Purcell, requiring the calculation of the temperature of a blackbody that corresponds to a frequency of 1420 MHz.

PREREQUISITES
  • Understanding of quantum mechanics, specifically hydrogen atom energy levels
  • Familiarity with Wien's law and its application in blackbody radiation
  • Knowledge of hyperfine transitions in atomic physics
  • Basic proficiency in physics calculations involving wavelengths and temperatures
NEXT STEPS
  • Study the derivation and application of the formula for electron energy in hydrogen atoms
  • Learn how to apply Wien's law to various blackbody radiation problems
  • Research hyperfine transitions and their significance in astrophysics
  • Explore the implications of cosmic background radiation on atomic transitions
USEFUL FOR

Students and enthusiasts in physics, particularly those interested in atomic transitions, blackbody radiation, and astrophysics. This discussion is beneficial for anyone seeking to deepen their understanding of quantum mechanics and its applications in stellar phenomena.

akance
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Hi! I really need some help
I'm really really not good at physics...so
Here it is

1) The electron energy of a hydrogen atom is given by -C/n^2 relative to zero energy at infinite separation between the electron and the proton (n is the principle quantum number, and C is a constant). For detection of the n=2 -> n=3 transition(656.3 nm in the Balmer Series), the electron is the ground state of the hydrogen atom needs to be excited first to the n=2 state. Calculate the wavelength (in nm) of the absorption line in the starlight corresponding to the n=1 -> n=2 transition.

2) According to Wien's law, the wavelength corresponding to the maximum light intensity emited from a blackbody at temperature T is given by (wavelength)(Temperature) = 2.9 mmK
Calculate the surface temperature of a star whose blackbody radiation has a peak intensity corresponding to the n=1 -> n=2 excitation of hydrogen

3) The ground state of hydrogen is split into two hyperfine levels due to the interaction between the magnetic moment of the proton and that of the electron. In 1951, Purcell discovered a spectral line at 1420 MHz due to the hyperfine transition of hydrogen in interstellar space. Hydrogen in interstellar space cannot be excited electronically by starlight. However, the cosmic background radiation, equivalent to 2.7K, can cause the hyperfine transition. Calculate the temperature of a blackbody whose peak intensity corresponds to the 1420 MHz transition

Can you please! help me with these 3 problems...! I am so confused!
 
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akance said:
Hi! I really need some help
I'm really really not good at physics...so
Here it is

1) The electron energy of a hydrogen atom is given by -C/n^2 relative to zero energy at infinite separation between the electron and the proton (n is the principle quantum number, and C is a constant). For detection of the n=2 -> n=3 transition(656.3 nm in the Balmer Series), the electron is the ground state of the hydrogen atom needs to be excited first to the n=2 state. Calculate the wavelength (in nm) of the absorption line in the starlight corresponding to the n=1 -> n=2 transition.

2) According to Wien's law, the wavelength corresponding to the maximum light intensity emited from a blackbody at temperature T is given by (wavelength)(Temperature) = 2.9 mmK
Calculate the surface temperature of a star whose blackbody radiation has a peak intensity corresponding to the n=1 -> n=2 excitation of hydrogen

3) The ground state of hydrogen is split into two hyperfine levels due to the interaction between the magnetic moment of the proton and that of the electron. In 1951, Purcell discovered a spectral line at 1420 MHz due to the hyperfine transition of hydrogen in interstellar space. Hydrogen in interstellar space cannot be excited electronically by starlight. However, the cosmic background radiation, equivalent to 2.7K, can cause the hyperfine transition. Calculate the temperature of a blackbody whose peak intensity corresponds to the 1420 MHz transition

Can you please! help me with these 3 problems...! I am so confused!

How much of these problems can you do?
 

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