# Atomic Hydrogen: Solving Homework on Thanksgiving - Help Needed

In summary, the conversation discusses quantizing the relation between energy and orbital quantum number for fixed electron energy in hydrogen-like atoms, using the Bohr model and the allowed values for r. The largest integer value of l consistent with the total energy is found to be lmax=n-1.
I spent my Thanksgiving trying to solve my homework and I will need some help:

1)For fixed electron energy ,the orbital quantum number l is limited to n-1.We can obtain this result from a semiclassical argument using the fact that the larges angular momentum describes circular orbits,where all kinetic energy is in orbital form.For hydrogen-like atoms U(x)=-(Zke^2)/r
and the energy in circular orbits becomes:

E=((|L|^2)/2mr^2)-(Zke^2)/r

Quantize this realtion using the rules of |L|=(l(l+1))^0.5 and E=-((ke^2)Z^2)/(2an^2),together with the Bohr result for the allowed values of r,to show that the largest integer value of l consistent with total energy i s lmax=n-1

solution:

ke^2)Z^2)/(2an^2)=((|L|^2)/2mr^2)-(Zke^2)/r and substituting |L|=(l(l+1))^0.5

ke^2)Z^2)/(2an^2)=(l(l+1))/2mr^2)-(Zke^2)/r

but i don't know what to do after this

You have to substitute for the r versus n dependence as given by Bohr.

Daniel.

When I use formula for Bohrs radius

my equation is :

n=(l(l+1))^05

and i don't know how i can from here get

lmax=n-1

You should have gotten an inequation. See if l_max=n will fit into your equation.

Daniel.

## What is atomic hydrogen and why is it important?

Atomic hydrogen is a single atom of hydrogen that exists in a neutral state. It is important because it is the simplest and most abundant element in the universe, making up approximately 75% of all matter.

## What are the properties of atomic hydrogen?

Atomic hydrogen has a single proton and a single electron, giving it an atomic number of 1. It also has a relatively low melting and boiling point and is highly reactive.

## How is atomic hydrogen used in solving homework on Thanksgiving?

Atomic hydrogen can be used in various chemical reactions and experiments, making it a useful tool for solving homework problems related to chemistry, physics, and other scientific fields.

## What are some common homework problems involving atomic hydrogen?

Some common homework problems involving atomic hydrogen include calculating its atomic mass, determining its electron configuration, and predicting its reactivity in different scenarios.

## What resources are available for help with homework involving atomic hydrogen?

There are many online resources available for help with homework on atomic hydrogen, including textbooks, study guides, and educational websites. Additionally, seeking help from a teacher or tutor can also be beneficial.

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