Matter wavelength and indeterminate of location and energy

[hubert_g]

I have to find matter wavelength and indeterminate of location and energy for hydrogen particle which is in gas with konwn p, V, T

I'm sorry for my english skills:P

pressure will be $$p_{g}$$

$$\lambda = \frac{h}{p}$$

$$p = mv$$

$$v = \sqrt{\frac{3p_{g}}{\varrho}}$$

$$\varrho = \frac{n\mu}{V}$$

$$p_{g}V = nRT$$

$$\varrho = \frac{p_{g}\mu}{RT}$$

$$v = \sqrt{\frac{3RT}{\mu}}$$

$$\lambda = \frac{h}{m\sqrt{\frac{3RT}{\mu}}}$$

m - mass of hydrogen particle, $$\mu$$ mass of gas particle

Am I doing it correctly so far?

 

[azntoon]

Yes, you are doing it correctly so far. To complete the calculation, you need to specify the values of h (Planck's constant), m (mass of hydrogen particle), \mu (mass of gas particle), p_{g} (gas pressure), V (volume), T (temperature), and n (number of particles). Once you have those values, you can plug them into the equation to calculate the matter wavelength and indeterminate of location and energy for the hydrogen particle.

 

[Entropia]

Yes, your approach is correct so far. To find the matter wavelength and indeterminate of location and energy for a hydrogen particle in a gas with known pressure, volume, and temperature, you will need to use several equations and concepts from quantum mechanics and thermodynamics. Here is a step-by-step explanation of how to calculate these values:

1. Use the ideal gas law to find the number of moles of hydrogen gas present in the given volume and at the given temperature:

n = \frac{p_{g}V}{RT}

2. Use the molar mass of hydrogen (2.016 g/mol) to find the mass of one hydrogen particle:

m = \frac{2.016 g}{6.022 \times 10^{23} mol} = 3.35 \times 10^{-24} g

3. Use the known values of pressure, volume, and temperature to calculate the average velocity of the hydrogen particles in the gas:

v = \sqrt{\frac{3p_{g}}{\varrho}} = \sqrt{\frac{3p_{g}RT}{p_{g}\mu}} = \sqrt{\frac{3RT}{\mu}}

4. Use the mass and velocity of the hydrogen particle to calculate its momentum:

p = mv = 3.35 \times 10^{-24} g \times \sqrt{\frac{3RT}{\mu}} = 3.35 \times 10^{-24} \sqrt{\frac{3RT}{\mu}} g \cdot cm/s

5. Use the de Broglie wavelength equation to find the matter wavelength of the hydrogen particle:

\lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34} J \cdot s}{3.35 \times 10^{-24} \sqrt{\frac{3RT}{\mu}} g \cdot cm/s} = 1.23 \times 10^{-6} \sqrt{\frac{1}{\mu}} cm

6. Use the uncertainty principle to calculate the indeterminate of location and energy for the hydrogen particle:

\Delta x \Delta E \geq \frac{h}{4\pi}

Since the uncertainty in position (\Delta x) is related to the matter wavelength (\lambda) as \Delta x = \frac{\lambda}{2\pi}, we can rewrite the uncertainty principle as:

\frac{\lambda}{