# Photons emitted by Hydrogen and helium atoms

• Elvis 123456789
In summary, excited hydrogen atoms can emit photons of various wavelengths. The maximum wavelength of the Balmer series is 656 nm and the minimum wavelength is 365 nm. The corresponding kinetic energy of the recoil hydrogen atom is 6.19 GeV. If the atom is changed from hydrogen to helium, the ratio of kinetic energies, KHe / KH, would be 4. The Rydberg formula for energy levels can be used for general hydrogenic atoms, with the inclusion of the Z² term. The specific R value for helium can be determined by looking at the definition of "R".
Elvis 123456789

## Homework Statement

An excited hydrogen atom can emit photons of various wavelengths.

a) What is the maximum wavelength of the Balmer series (in nm) (5pt)

b) What is the minimum wavelength of the Balmer series (in nm) (5pt)

c) Corresponding to part b), what is the kinetic energy of the recoil hydrogen atom, in the unit of eV? ( mH = 938MeV / c 2 )10pt)

d) Assume the helium atom (Z=2) has the mass that is 4 times of hydrogen, what should happen to your answer to part c), if the atom is changed from hydrogen to helium. Show you results in terms of KHe / KH = ? (10pt)

## Homework Equations

1/λ = R (1/nf2 -1/ni2)

R = 1.097*107 m-1

mv = Ephoton/c ----> due to momentum conservation

KE = 0.5 * (mv)2 * 1/m

## The Attempt at a Solution

a.) max wavelength happens when energy level goes from n = 3 to n = 2

λmax = 656 nm

b.) the min wavelength happens when the energy level goes from n = ∞ to n = 2

λmin = 365 nm

c.) Ephoton = h*c/λmin = 3.41 eV
mH = 938 MeV/c2

KEH = 6.19 GeV

d.) I'm not sure how to do this part since the rydberg equation is meant to be used with hydrogen

You have a derivation for energy levels of general hydrogenic atoms which has Z in it.
The Rydberg formula is derived from this with Z=1.

We never covered this in class but I found the equation with the included Z2 term in it. But would I then use the same R value or is there some specific helium R?

You can answer that yourself by looking at the definition of "R".
Note: you almost certainly covered this in class.
Where did you find the equation with the R value in it?

## 1. What is the difference between photons emitted by Hydrogen and helium atoms?

Photons emitted by Hydrogen and helium atoms have different wavelengths, which correspond to different energy levels. Hydrogen emits photons with longer wavelengths than helium, as it has a larger atomic number and therefore more electrons and energy levels.

## 2. How are photons emitted by Hydrogen and helium atoms produced?

Photons are emitted when electrons in the atoms drop from a higher energy level to a lower one. In Hydrogen, the electrons can drop from any energy level to the first energy level, while in helium, the electrons can only drop from the second energy level to the first.

## 3. What is the significance of the emission and absorption of photons by Hydrogen and helium atoms?

The emission and absorption of photons by Hydrogen and helium atoms play a crucial role in understanding the behavior and properties of these atoms. It helps in studying the energy levels, electron transitions, and spectral lines of these atoms, which are important for various fields of science, including astrophysics and quantum mechanics.

## 4. How do the photons emitted by Hydrogen and helium atoms contribute to the formation of elements in the universe?

The photons emitted by Hydrogen and helium atoms play a significant role in the formation of elements in the universe through the process of nucleosynthesis. The fusion of Hydrogen atoms in stars produces helium and releases photons, which then react with other atoms to form heavier elements.

## 5. Can the emission of photons by Hydrogen and helium atoms be controlled or manipulated?

Yes, the emission of photons by Hydrogen and helium atoms can be controlled and manipulated through various techniques such as laser excitation, electric fields, and magnetic fields. These methods allow scientists to study and control the behavior of these atoms and their emitted photons, leading to advancements in technology and research.

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