Answer :
The de Broglie wavelength of the bullet travelling at 1265 miles per having a mass of 6.45 g is 6.13 x 10⁻³³ m
De Broglie wavelength is the relation between the momentum and mass of an object. It is inversely proportional to its force. The de Broglie wavelength of an object is given by
λ = h
p
where,
λ = De Broglie wavelength
h = Planck's constant
p = momentum = mass x velocity
First, we will convert velocity fro miles per hour to m s⁻¹
Velocity = 1265 miles per hour
1 mile = 1.60 km
1265 x 1.60 = 2024
It is multiplied by 1 to convert into m s⁻¹
60 x 60
It gives = 16.86 m s⁻¹
Mass is converted from gram to kilogram
m = 6.45 g = 0.00645 kg or 6.45 x 10⁻³ kg
The momentum of bullet is p, which is
p = mv
p = 0.00645 kg x 16.86 m s ⁻¹
p = 0.108 kgms⁻¹
λ = h
p
where,
h is planck's constant = 6.63 x 10⁻³⁴ m²kg⁻¹
p is the momentum = 0.108 kgms⁻¹
λ is the de Broglie wavelength
putting the values,
λ = 6.63 x 10⁻³⁴ m²kg⁻¹
0.108 kgms⁻¹
λ = 6.13 x 10⁻³³ m
To learn more about wavelength,
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