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mateomy

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Thanks.

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- Thread starter mateomy
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In summary, the conversation discusses the relationship between the de Broglie wavelength and the average separation between particles in a gas. It is stated that the atoms in a gas can be treated as classical particles if their de Broglie wavelength is much smaller than the average separation between the particles. The conversation then asks for a comparison between the de Broglie wavelength and average separation in a container of monatomic helium gas at 1.00 atm pressure and room temperature. It is suggested to use the ideal gas law to solve the problem. Finally, the conversation seeks a hint to solve the problem, with a reminder to include volume per particle in the calculation.

- #1

mateomy

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Thanks.

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- #2

TSny

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Hello. My hint would be "ideal gas law". You don't need volume, but you do need volume per particle.

- #3

mateomy

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Awesome. I thought it had something to do with that. Thanks a lot.

- #4

DJSedna

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I'm currently stuck on this problem staring at a blank page. I understand that the De Broglie Wavelength formula is necessary here as well as the Ideal Gas Law, but I must be missing something. Can anyone give me a hint just to get me on track with this problem?

Thanks in advance.

- #5

paranormal

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The de Broglie wavelength is given by the equation λ = h/mv, where h is Planck's constant, m is the mass of the particle, and v is its velocity. In the case of atoms in a gas, their velocity can be approximated by the average speed of the gas molecules, which is given by the root mean square velocity, vrms = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

For monatomic helium gas at 1.00 atm pressure and 20 degrees C (293 K), the molar mass is 4.003 g/mol. Plugging in these values, we get vrms = √(3*8.314 J/mol*K*293 K / 0.004003 kg/mol) = 1404 m/s.

Now, to calculate the average separation between the atoms, we can use the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, and R is the gas constant. Rearranging for volume, we get V = nRT/P. Assuming a container of 1 mole of monatomic helium gas, we get V = (1 mol * 8.314 J/mol*K * 293 K) / (1.00 atm * 101325 Pa/atm) = 2.44 x 10^-3 m^3.

The volume of the container can also be calculated by taking the average separation between the atoms and multiplying it by the number of atoms in the gas. The number of atoms can be calculated by dividing the mass of the gas (1 mole * 4.003 g/mol = 4.003 g) by the molar mass (4.003 g/mol), giving us 6.02 x 10^23 atoms. Therefore, the average separation between the atoms is V/n = (2.44 x 10^-3 m^3) / (6.02 x 10^23 atoms) = 4.06 x 10^-27 m.

Comparing this to the calculated de Broglie wavelength, which is given by λ = h/mv = (6.626 x 10^-34 J*s) / (4.003 x 10^-3 kg * 1404 m/s) = 1.49

The De Broglie wavelength is a concept in quantum mechanics that describes the wave-like behavior of particles, such as electrons. It is named after physicist Louis de Broglie, who proposed that all particles have a wavelength associated with them.

The De Broglie wavelength can be calculated using the equation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity. This equation is also known as the de Broglie relation.

The De Broglie wavelength is significant because it provides a way to describe the dual nature of particles as both particles and waves. It also helps to explain phenomena such as diffraction and interference, which were previously only understood in terms of waves.

All particles, including subatomic particles like electrons, atoms, and molecules, have a De Broglie wavelength. However, the wavelength is most noticeable for particles with very small masses, such as electrons, due to their high velocities.

No, the De Broglie wavelength cannot be directly observed. It is a theoretical concept that helps to explain the behavior of particles at the quantum level. However, the effects of the De Broglie wavelength can be observed through experiments, such as electron diffraction, which demonstrate the wave-like behavior of particles.

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