# Electrons bombard gaseous hydrogen - photon energies emitted?

• Flucky
In summary: V electrons and the question asks for the photon energies that will be emitted. The equation for calculating the energy difference is given and rearranged to find the final state of the electron, which is n=4. From this, it can be determined that the electron can transition to n=4, n=3, and n=2 states, with corresponding photon energies of 12.75 eV, 12.09 eV, and 10.2 eV respectively. It is necessary to write down all possible photon energies that can be emitted from this process.
Flucky

## Homework Statement

A beam of 13.0 eV electrons is used to bombard gaseous hydrogen in ground state.
What photon energies will be emitted?

## Homework Equations

ΔE = -13.6 ($\frac{1}{n^{2}_{f}}$ - $\frac{1}{n^{2}_{i}}$)

However hydrogen is in the ground state therefore n_i= 1:

ΔE = -13.6 ($\frac{1}{n^{2}_{f}}$ - 1)

## The Attempt at a Solution

Rearranging the above equation I got n_f = 4.76.

Am I correct in saying "the photon can be emitted from a maximum energy state of n=4"?
I'm unsure how to word it.

WRT the initial question, it asks what photon energies will be emitted so would I have to write them all down?

ie

4$\rightarrow$3 = 0.66 ev
4$\rightarrow$2 = 2.55 ev
4$\rightarrow$1 = 12.75 ev

3$\rightarrow$2 = 1.89 ev
3$\rightarrow$1 = 12.09 ev

2$\rightarrow$1 = 10.2 ev

I'm unsure how to word it.

13 eV is enough to reach the n=3 level which has an energy of 12.09 eV above ground state.
13 eV is enough to reach the n=4 level which has an energy of 12.75 eV above ground state.
13 eV is not enough to reach the n=5 level which has an energy of 13.056 eV above ground state.

it asks what photon energies will be emitted so would I have to write them all down?

Yes.
As you saw, there are not so many lines.
You might present them in a level diagram, or in a table, if you like to present things ...

1 person
Thanks maajdl

## 1. What is the process of electrons bombarding gaseous hydrogen?

Electrons bombarding gaseous hydrogen refers to a phenomenon in which high-energy electrons collide with gaseous hydrogen atoms, resulting in the transfer of energy from the electrons to the atoms.

## 2. How is energy transferred from electrons to gaseous hydrogen atoms?

The energy transfer from electrons to gaseous hydrogen atoms occurs through a process called excitation, where the high-energy electrons cause the hydrogen atoms to move to a higher energy state. This excess energy is then released in the form of photons.

## 3. What is the significance of photon energies emitted in this process?

The photon energies emitted in the process of electrons bombarding gaseous hydrogen provide valuable information about the energy levels of the hydrogen atoms. This information can be used to study the structure and behavior of the atoms and can also be used in various scientific and technological applications.

## 4. How are the photon energies emitted measured?

The photon energies emitted in this process can be measured using a device called a spectrometer. This instrument is designed to detect and measure the wavelengths and energies of photons emitted by atoms or molecules.

## 5. What are the potential applications of studying electrons bombarding gaseous hydrogen?

Studying electrons bombarding gaseous hydrogen has various potential applications in fields such as astrophysics, plasma physics, and materials science. It can also be used to understand the behavior of atoms and molecules in different environments and to develop new technologies such as lasers and lighting sources.

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