# How Do You Calculate the Minimum Wavelength to Ionize Hydrogen Atoms?

• xregina12
In summary, the conversation discusses a question about quantum mechanics homework, specifically the calculation of the minimum wavelength of light that will ionize H atoms in their ground state. Part b) also involves calculating the speed of an electron before colliding with the H atom. The conversation provides suggestions and advice on how to approach the question and solve it.
xregina12
Hi, below is a question from my first quantum mechanics homework. I haven't taken quantum mechanics before and I don't how to approach the question exactly. For part a, I believe I can use the equation Emax=1/2mv^2=hv-hvo. vo=binding energy. For the minum wavelength of light, do I assume the electrons emitted have no velocity after emission and set hv-hvo=0? Can someone please guide me with this problem or give me some suggestions? I would really really appreciate this!

7. Quantum mechanics predicts that the binding energy of the ground state of the H atom is -
13.6 eV. Insight into the magnitude of this quantity is gained by considering several methods by
which it can be measured.
a) Calculate the minimum wavelength of light that will ionize H atoms in their ground state.
b) Assume the H atom is ionized by collision with an electron that transfers all its kinetic energy
to the H atom in the ionization process. Calculate the speed of the electron before the collision.
Express your answer in m s-1 and in miles hour--1.

Firstly, I believe part a) should read maximum wavelength, not minimum.

For part a), firstly work out what the minimum photon energy needs to be to ionise the H atom, then use E = hc/lambda to determine the corresponding wavelength.

For part b), determine the kinetic energy of the incident electron then work out the velocity using KE = 1/2 mv^2.

Claude.

## What is quantum mechanics?

Quantum mechanics is a branch of physics that describes the behavior of particles at the atomic and subatomic level. It is a theoretical framework that explains the fundamental properties and interactions of matter and energy.

## What are the basic principles of quantum mechanics?

The basic principles of quantum mechanics include superposition, wave-particle duality, and uncertainty. Superposition states that particles can exist in multiple states simultaneously, while wave-particle duality states that particles can exhibit characteristics of both waves and particles. Uncertainty refers to the inherent limitations in measuring the properties of particles at the quantum level.

## How does quantum mechanics differ from classical mechanics?

Quantum mechanics differs from classical mechanics in that it describes the behavior of particles at a much smaller scale. Classical mechanics only applies to larger objects, while quantum mechanics applies to particles such as atoms and subatomic particles. Additionally, classical mechanics is deterministic, meaning that the future behavior of a system can be predicted with certainty, while quantum mechanics is probabilistic, meaning that it can only predict the probability of a particle's behavior.

## What is the significance of quantum mechanics?

Quantum mechanics has had a significant impact on our understanding of the universe and has led to many technological advancements, such as transistors, lasers, and MRI machines. It also plays a crucial role in modern fields such as quantum computing and quantum cryptography.

## What are some real-world applications of quantum mechanics?

Some real-world applications of quantum mechanics include transistors in electronic devices, lasers in medical and industrial applications, and cryptography for secure communication. Other potential applications include quantum computing for faster and more efficient data processing, and quantum sensors for improved precision in measurements.

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