Among the elementary subatomic particles of physics is the muon, which decays within a few microseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at 8.85 * 105 cm/s.

Verified step by step guidance

1. Step 1: Understand the problem. The de Broglie wavelength is given by the equation λ = h / (m*v), where h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle. We are given the velocity and the mass of the muon in terms of the mass of an electron.
2. Step 2: Convert the mass of the muon to kilograms. The mass of an electron is approximately 9.11 * 10^-31 kg. Therefore, the mass of the muon is 206.8 times this value.
3. Step 3: Convert the velocity of the muon to meters per second. The given velocity is in centimeters per second, so we need to divide by 100 to get meters per second.
4. Step 4: Substitute the values into the de Broglie wavelength equation. Planck's constant h is approximately 6.63 * 10^-34 Js.
5. Step 5: Solve the equation for λ. This will give you the de Broglie wavelength associated with a muon traveling at the given velocity.

Key Concepts

De Broglie Wavelength

The de Broglie wavelength is a concept in quantum mechanics that describes the wave-like behavior of particles. It is given by the formula λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. For a particle with mass m and velocity v, momentum p can be expressed as mv. This concept is crucial for understanding the wave-particle duality of matter.

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity (p = mv). In the context of subatomic particles like muons, momentum plays a significant role in determining their behavior and properties. Understanding momentum is essential for calculating the de Broglie wavelength, as it directly influences the wave characteristics of the particle.

Planck's Constant

Planck's constant (h) is a fundamental constant in quantum mechanics, approximately equal to 6.626 x 10^-34 Js. It relates the energy of a photon to its frequency and is a key factor in the de Broglie wavelength formula. This constant signifies the scale at which quantum effects become significant, making it essential for calculations involving the wave properties of particles like muons.