). An electron, a proton, and a neutron have the same de Broglie wavelength. Which one of the following statements regarding the speeds of these particles is true? a. The electron has the highest speed of these three particles. b. The proton has the highest speed of these three particles. c. The neutron has the highest speed of these three particles. d. The proton and the neutron both have the highest speeds. e. All three particles have the same speed.
Particle Theory of Light
The particle theory of light was the proposal made by Newton in 1704 in his treatise Opticks. This is the most basic light theory, in which light is thought to be made up of microscopic particles known as "corpuscles" and that's why this particle theory of light is also named as Corpuscular theory of light.
Stopping Potential
In an experiment conducted by Heinrich Hertz, an apparatus was made where the incident light was made to fall on the metallic plate, it was discovered that metals emit electrons. The surface electrons are bound to metals with a minimum amount of energy and some of the incident photos enter the surface, they undergo collision with the atoms of the metal, they get absorbed and emit energy to an election, making it photoelectron, where the collision between the photons and electrons ejects the electrons out of the metal and with a negatively charged electron, causes photocurrent and when this current passes it creates an electric field where there is a potential difference at the output due to the anode and cathode of the electrode of the apparatus. This study involves the theory of Quantum physics and electromagnetism involving electromagnetic radiation and electromagnetic wave theory.
Quantization of Charges
An electron is a negatively charged subatomic particle either attached to an an atom or sticks to the nucleus of the atom. Electrons exert the negative charge that tries to balance the positive charge of the nucleus.
![### Educational Resource on de Broglie Wavelength and Particle Speeds
#### Question 10
Consider an electron, a proton, and a neutron that all have the same de Broglie wavelength. Which of the following statements regarding the speeds of these particles is true?
a. The electron has the highest speed of these three particles.
b. The proton has the highest speed of these three particles.
c. The neutron has the highest speed of these three particles.
d. The proton and the neutron both have the highest speeds.
e. All three particles have the same speed.
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**Explanation:**
The de Broglie wavelength (\(\lambda\)) of a particle is given by the equation:
\[ \lambda = \frac{h}{p} \]
where \(h\) is the Planck constant and \(p\) is the momentum of the particle. Since momentum (\(p\)) is the product of mass (\(m\)) and velocity (\(v\)), we have:
\[ \lambda = \frac{h}{mv} \]
Given that the electron, proton, and neutron have the same de Broglie wavelength, \(\lambda\), it implies:
\[ \frac{h}{m_e v_e} = \frac{h}{m_p v_p} = \frac{h}{m_n v_n} \]
where \(m_e\), \(m_p\), and \(m_n\) are the masses of the electron, proton, and neutron respectively, and \(v_e\), \(v_p\), and \(v_n\) are their respective speeds.
Since the mass of an electron is significantly less than the masses of a proton and a neutron, to maintain the same de Broglie wavelength, the electron must have a higher speed. Therefore, the correct answer is:
**a. The electron has the highest speed of these three particles.**
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Understanding these principles is fundamental in quantum mechanics and helps in analyzing various physical systems at the microscopic level. This question exemplifies the relationship between mass, speed, and wavelength as described by wave-particle duality in quantum physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0959128f-1417-4f4f-bd20-8f81c7fe5d61%2F3f2aa6b7-65f3-4947-b787-98e7d16eafe4%2Fzir36g.png&w=3840&q=75)
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