According to the idea of wave particle duality, which of the following items has a wavelength? Choose all that apply.
An electron moving at 2.80 m/s.
A planet moving at 180,000 km/hr.
A gas molecule moving at 515 m/s
A person running at 10 mi/hr.
i think its A and D is it correct?
I think it is indeed A and D but also is B and C. It it is an "it" it has a wavelength :)
Yes, you are correct. According to the idea of wave-particle duality, both particles and matter can exhibit wave-like properties, including having a wavelength. Therefore, an electron moving at 2.80 m/s (option A) and a person running at 10 mi/hr (option D) both have a wavelength associated with them.
According to the concept of wave-particle duality, both particles and objects can exhibit wave-like behavior. However, for an object to have a wavelength, it must possess momentum and be associated with the de Broglie wavelength.
The de Broglie wavelength, denoted by λ, is determined using the following equation: λ = h / p, where h is the Planck constant (approximately 6.626 x 10^-34 J*s) and p is the momentum of the object.
Let's calculate the momentum for each of the given items to determine if they have a wavelength.
For an electron moving at 2.80 m/s, we can use the mass and velocity of the electron to find its momentum. The mass of an electron is approximately 9.109 x 10^-31 kg. So, the momentum (p) of the electron is equal to the mass (m) multiplied by the velocity (v): p = m * v.
By substituting the values, p = (9.109 x 10^-31 kg) * (2.80 m/s) ≈ 2.555 x 10^-30 kg*m/s.
Now, we can calculate the de Broglie wavelength using the equation λ = h / p: λ = (6.626 x 10^-34 J*s) / (2.555 x 10^-30 kg*m/s) ≈ 2.59 x 10^-4 meters.
Therefore, the electron moving at 2.80 m/s has a wavelength.
Now let's consider the other items:
For a planet moving at 180,000 km/hr, since it is a macroscopic object, we assume its mass to be significantly larger than that of an electron. Thus, its momentum is significantly larger. However, the wavelength is inversely proportional to momentum, so for large objects, the wavelength becomes extremely small and practically negligible. Therefore, we can conclude that the planet does not have a measurable wavelength.
For a gas molecule moving at 515 m/s, we need to know the mass of the gas molecule to calculate its momentum. As the mass of a gas molecule is typically very small, we assume it to be the same order of magnitude as the mass of an electron. So, the gas molecule's momentum will also be on the same order of magnitude as that of the electron. Therefore, the gas molecule should have a measurable wavelength based on the de Broglie equation.
For a person running at 10 mi/hr, the person's mass is significantly larger than that of an electron or a gas molecule. So, their momentum will be several orders of magnitude larger. As mentioned before, the wavelength is inversely proportional to momentum, so for large objects like a person, the wavelength becomes extremely small and practically negligible. Hence, we can conclude that the person running at 10 mi/hr does not have a measurable wavelength.
In summary, based on the concept of wave-particle duality and the de Broglie wavelength equation, the items that have a measurable wavelength are: an electron moving at 2.80 m/s (option A) and a gas molecule moving at 515 m/s (option C).