Measuring Displacement in Hydrogen Atoms: Exploring d

[iLIKEstuff]

Homework Statement

Part A)
Assume you have a capacitor with H-atom gas with a separation of the plates of $${10}^{-4}$$meter and a voltage of 20 volts across the capacitor. Calculate the distance "d" (the displacement of the charges in the atom), where the induced dipole of the hydrogen atom is $$\mu = {e}^{-} d$$

Part B)

Apparently people have measured this dipole, and therefore are capable of estimating this
distance “d”. Considering the size of “d” that you calculated, explain how it is possible to
“observe” (through the measurement of $$\mu$$) the size of “d”.

Homework Equations

The Attempt at a Solution

For Part A) I calculated $$d=\frac{\alpha \cdot \frac{V}{dist}}{q_e}=2.059 \cdot {10}^{-17} meters$$

where
$$\alpha = \text{polarizability} = 1.649 \cdot {10}^{-41}$$
$$V= 20 volts$$
$$dist= {10}^{-4} meters$$
$$q_e= 1.602 \cdot {10}^{-19} coulombs$$

What I don't know is Part B) how do people measure such a small value and estimate the distance??

Thanks for the help.

 

[Jhero]

Thank you for your question. It is indeed fascinating that scientists are able to measure such small values and estimate distances that are not directly observable. Let me try to explain this in more detail.

First, let's clarify what we mean by the distance "d" in this problem. We are talking about the displacement of the charges in the hydrogen atom, which is related to the induced dipole moment \mu. This distance is not a physical distance between two points, but rather a measure of the separation between the positive and negative charges within the atom. This separation is caused by the external electric field created by the capacitor.

Now, how do scientists measure this dipole moment and estimate the distance "d"? One way is through spectroscopy, a technique that allows us to study the interaction of matter with electromagnetic radiation. In the case of the hydrogen atom, we can use different types of spectroscopy, such as microwave or infrared spectroscopy, to measure the energy levels of the atom. These energy levels are directly related to the dipole moment of the atom, and by measuring them, we can calculate the dipole moment and hence the distance "d".

Another way to measure this dipole moment is through dielectric constant measurements. Dielectric constant is a measure of how well a material can store electrical energy. In the case of the hydrogen atom, the induced dipole moment affects the dielectric constant of the gas between the plates of the capacitor. By measuring the change in dielectric constant, we can calculate the dipole moment and hence the distance "d".

In summary, scientists use various techniques such as spectroscopy and dielectric constant measurements to indirectly measure the dipole moment of the hydrogen atom and estimate the distance "d". These techniques rely on the fundamental principles of physics and allow us to study and understand the behavior of matter at the atomic level.

I hope this helps to answer your question. Keep asking questions and exploring the fascinating world of science!