The wavelength of the golf ball is 2.328×10⁻³⁴m.
All moving particles with mass have a matter wave associated with it. These matter waves are called deBroglie waves.
The deBroglie wavelength λ of a particle is given by,
[tex]\lambda=\frac{h}{mv}[/tex]
Here, h is the Planck's constant, m is the mass of the ball and v is its velocity.
Calculate the deBroglie wavelength of the moving golf ball by substituting 6.626×10⁻³⁴J s for h, 45.9×10⁻³kg for m and 62.0 m/s for v.
[tex]\lambda=\frac{h}{mv}\\ =\frac{6.626*10^-^3^4Js}{(45.9*10^-^3kg)(62.0m/s)} \\ =2.328*10^-^3^4m[/tex]
The wavelength of the golf ball is 2.328×10⁻³⁴m.
As the question depicts the mass of golf ball is 45.9grams and is leaving with the speed of 62.0m/sec, the wavelength is [tex]2.328\times10^{-34}[/tex]m
Wavelength is the distance between the successive crests of the wave, especially in the sound waves.
The wavelength is determined by the de Broglie formula which is given below,
[tex]\lambda=\frac{h}{mv}[/tex]
here,
h= Plank's constant = [tex]6.626\times 10^{-34} Jsec[/tex]
m= Mass of the object = 45.9 grams = [tex]45.9\times10^{-3}[/tex]
v= Velocity of the object = 62.0 m/sec
so,
[tex]\lambda=\frac{6.626\times10^{-34} }{(45.9\times10^{-3})(62.0) }[/tex]
[tex]\lambda=2.328\times10^{-34}[/tex] m
So, the corresponding wavelength is [tex]2.328\times10^{-34}[/tex]m
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