Physics, 22.10.2019 23:30, ricesonice5

What is the wavelength of the matter wave associated with a proton moving at 377377 m/s? wavelength of proton matter wave: mm what is the wavelength of the matter wave associated with a 159159 kg astronaut (including her spacesuit) moving at the same speed? wavelength of astronaut matter wave: mm what is the wavelength of the matter wave associated with earth moving along its orbit around the sun? wavelength of earth matter wave: m

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answered: lescoto9035

This question can be used using the concept of de Broglie's wavelength and matter-wave.

a) Wavelength of matter-wave associated is "1.052 x 10⁻⁶ mm".

b) Wavelength of matter-wave associated with an astronaut is "1.105 x 10⁻³⁵ mm".

c) Wavelength of matter-wave is associated with Earth "3.68 x 10⁻⁶³ m".

The concept of matter-wave states that every matter has a certain wavelength due to its motion. This wavelength can be found using the formula of de Broglie's wavelength.

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

where,

λ = de Broglie's Wavelength

h = Plank's Constant = 6.625 x 10⁻³⁴ J.s

m = mass

v = speed

For the proton:

m = 1.67 x 10⁻²⁷ kg

v = 377 m/s (correction, double written in question)

$\lambda = \frac{6.625\ x\ 10^{-34}\ J.s}{(1.67\ x\ 10^{-27}\ kg)(377\ m/s)}$

λ = 1.052 x 10⁻⁹ m = 1.052 x 10⁻⁶ mm

For the astronaut:

m = 159 kg (correction, double written in question)

v = 377 m/s (correction, double written in question)

$\lambda = \frac{6.625\ x\ 10^{-34}\ J.s}{(159\ kg)(377\ m/s)}$

λ = 1.105 x 10⁻⁻³⁸ m = 1.105 x 10⁻³⁵ mm

For the Earth moving around Sun:

m = 6 x 10²⁴ kg

v = 29951.68 m/s

$\lambda = \frac{6.625\ x\ 10^{-34}\ J.s}{(6\ x\ 10^{24}\ kg)(29951.68\ m/s)}\\\\$

λ = 3.68 x 10⁻⁶³ m

Learn more about de Broglie's wavelength here:

link

The attached picture shows the formula of de Broglie's wavelength.

answered: blondielocks2002

1) $1.05\cdot 10^{-9} m$

The wavelength of the matter wave (also called de Broglie wavelength) of an object is given by

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

where

$h=6.63\cdot 10^{-34} Js$ is the Planck constant

m is the mass of the object

v is its velocity

For a proton, we have:

$m=1.67\cdot 10^{-27} kg$

and the velocity of this proton is

v=377 m/s

So, its de Broglie's wavelength is:

$\lambda=\frac{6.63\cdot 10^{-34}}{(1.67\cdot 10^{-27})(377)}=1.05\cdot 10^{-9} m$

2) $1.11\cdot 10^{-38} m$

We can use again the same equation:

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

where in this case we have:

m = 159 kg is the mass of the astronaut + spacesuit

v = 377 m/s is the velocity of the astronaut

Substituting into the equation,

$\lambda=\frac{6.63\cdot 10^{-34}}{(159)(377)}=1.11\cdot 10^{-38} m$

3) $3.70\cdot 10^{-63} m$

Similarly, we can use the same equation:

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

where in this case we have: $m=5.98\cdot 10^{24}kg$ is the Earth's mass

v=30 km/s = 30000 m/s is the velocity of the Earth around the Sun

Substituting,

$\lambda=\frac{6.63\cdot 10^{-34}}{(5.98\cdot 10^{24})(30000)}=3.70\cdot 10^{-63} m$

What is the wavelength of the matter wave associated with a proton moving at 377377 m/s? wavelength

answered: Guest

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answered: Guest

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