A proton in a linear accelerator has a de Broglie wavelength of 132 pm. What is the speed of the proton?

검증된 단계별 안내

Identify the de Broglie wavelength formula: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant, \( m \) is the mass of the particle, and \( v \) is the velocity.

Rearrange the formula to solve for velocity \( v \): \( v = \frac{h}{m\lambda} \).

Substitute the known values into the equation: Planck's constant \( h = 6.626 \times 10^{-34} \) Js, the mass of a proton \( m = 1.673 \times 10^{-27} \) kg, and the wavelength \( \lambda = 132 \times 10^{-12} \) m.

Calculate the velocity \( v \) using the rearranged formula.

Ensure the units are consistent and check the calculation for any errors.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

de Broglie Wavelength

The de Broglie wavelength is a fundamental concept in quantum mechanics that relates the wavelength of a particle to its momentum. 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. This concept illustrates the wave-particle duality of matter, indicating that particles like protons exhibit wave-like properties.

Momentum

Momentum is a vector quantity defined as the product of an object's mass and its velocity (p = mv). In the context of particles, momentum plays a crucial role in determining their behavior in both classical and quantum mechanics. For a proton, knowing its mass allows us to calculate its momentum when its speed is known, which is essential for finding the speed from the de Broglie wavelength.

Planck's Constant

Planck's constant (h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It has a value of approximately 6.626 x 10^-34 Js. In the context of the de Broglie wavelength, Planck's constant is used to calculate the momentum of particles, linking their wave-like properties to their physical characteristics, such as speed.