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

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.

where,

λ = de Broglie's Wavelength

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

m = mass

v = speed

a)

For the proton:

m = 1.67 x 10⁻²⁷ kg

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

λ = 1.052 x 10⁻⁹ m = 1.052 x 10⁻⁶ mm

b)

For the astronaut:

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

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

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

c)

For the Earth moving around Sun:

m = 6 x 10²⁴ kg

v = 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.

1)

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

where

is the Planck constant

m is the mass of the object

v is its velocity

For a proton, we have:

and the velocity of this proton is

So, its de Broglie's wavelength is:

2)

We can use again the same equation:

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,

3)

Similarly, we can use the same equation:

where in this case we have: is the Earth's mass

is the velocity of the Earth around the Sun

Substituting,

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