A 0.22-caliber handgun fires a 27-g bullet at a velocity of 765 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?
3.2x10^-35
To calculate the de Broglie wavelength of the bullet, we can use the equation:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck constant (6.626 x 10^-34 J·s), and p is the momentum of the bullet.
To find the momentum, we can use the equation:
p = m * v
where m is the mass of the bullet and v is its velocity.
Given:
Mass of the bullet (m) = 27 g = 0.027 kg
Velocity of the bullet (v) = 765 m/s
Let's calculate the momentum first:
p = m * v
= 0.027 kg * 765 m/s
= 20.755 kg·m/s
Now, we can calculate the de Broglie wavelength:
λ = h / p
= (6.626 x 10^-34 J·s) / (20.755 kg·m/s)
≈ 3.186 x 10^-36 m
The de Broglie wavelength of the bullet is approximately 3.186 x 10^-36 meters.
Regarding the significance of the wave nature of matter for bullets, in the case of macroscopic objects like bullets, the wavelength is extremely small, making the wave nature practically negligible. The wave-particle duality of matter becomes more apparent at the atomic and subatomic levels, such as the behavior of particles in quantum mechanics. For everyday objects, such as bullets, their wave nature is not observable or relevant in the context of their motion.
To calculate the de Broglie wavelength of the bullet, we can use the equation:
λ = h / p
Where:
λ = de Broglie wavelength
h = Planck's constant (h = 6.626 x 10^-34 J*s)
p = momentum of the bullet
First, we need to calculate the momentum of the bullet:
p = m * v
Where:
m = mass of the bullet (in kg)
v = velocity of the bullet (in m/s)
Given that the mass of the bullet is 27 grams (which is equivalent to 0.027 kg) and the velocity is 765 m/s, we can calculate the momentum:
p = (0.027 kg) * (765 m/s)
Now, we can calculate the de Broglie wavelength by dividing Planck's constant by the momentum:
λ = (6.626 x 10^-34 J*s) / (0.027 kg * 765 m/s)
Once you perform this calculation, you will find the de Broglie wavelength of the bullet.
Now, to determine if the wave nature of matter is significant for bullets, we need to compare the de Broglie wavelength with the typical size of the objects involved. In the case of a bullet, which is typically a few centimeters in size, the de Broglie wavelength is likely to be extremely small compared to the size of the bullet. Therefore, for everyday objects like bullets, the wave nature of matter is not significant and does not have observable effects.