1.
Complete the following statement: According to the de Broglie relation, the wavelength of a "matter" wave is inversely proportional to
Correct Answer
C. The momentum of the particle.
Explanation
According to the de Broglie relation, the wavelength of a "matter" wave is inversely proportional to the momentum of the particle. This means that as the momentum of the particle increases, the wavelength of the wave decreases. Conversely, as the momentum decreases, the wavelength increases. This relation is derived from the wave-particle duality concept, which suggests that particles can exhibit wave-like properties and have associated wavelengths. The de Broglie relation provides a mathematical relationship between the wavelength and momentum of a particle.
2.
What is the de Broglie wavelength of an electron (m = 9.11 ´ 10^{-}^{31} kg) in a 5.0 ´ 10^{3}-volt X-ray tube?
Correct Answer
C. 0.017 nm
Explanation
The de Broglie wavelength of a particle can be calculated using the equation λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. In this case, we are given the mass of the electron and the voltage of the X-ray tube. Since the voltage can be used to calculate the kinetic energy of the electron, we can then use the kinetic energy to calculate the momentum of the electron. By substituting the values into the equation, we find that the de Broglie wavelength of the electron is 0.017 nm.
3.
Determine the de Broglie wavelength of a neutron (m = 1.67 ´ 10^{-}^{27} kg) which has a speed of 5.0 m/s.
Correct Answer
A. 79 nm
Explanation
The de Broglie wavelength of a particle is given by the equation λ = h / mv, where h is the Planck's constant, m is the mass of the particle, and v is its velocity. In this question, we are given the mass of the neutron (1.67 × 10-27 kg) and its speed (5.0 m/s). By plugging these values into the equation, we can calculate the de Broglie wavelength of the neutron, which is found to be 79 nm.
4.
The de Broglie wavelength of an electron (m = 9.11 ´ 10^{-}^{31} kg) is 1.2 ´ 10^{-}^{10} m. Determine the kinetic energy of the electron.
Correct Answer
C. 1.7 x 10^-17 J
Explanation
The de Broglie wavelength of an electron is given by the equation λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the electron. The momentum of an object is given by the equation p = m * v, where m is the mass of the object and v is its velocity. Rearranging the equations, we can solve for the velocity of the electron, v = p / m. Substituting this value into the equation for kinetic energy, KE = 1/2 * m * v^2, we can calculate the kinetic energy of the electron using the given values. The correct answer is 1.7 x 10^-17 J.
5.
What happens to the de Broglie wavelength of an electron if its momentum is doubled?
Correct Answer
E. The wavelength decreases by a factor of 2.
Explanation
When the momentum of an electron is doubled, its de Broglie wavelength decreases by a factor of 2. This is because the de Broglie wavelength is inversely proportional to the momentum of the particle. When the momentum is doubled, the wavelength decreases by half.
6.
The Hubble Space Telescope has an orbital speed of 7.56 ´ 10^{3} m/s and a mass of 11,600 kg. What is the de Broglie wavelength of the telescope?
Correct Answer
E. 7.56 x 10^-42 m
Explanation
The de Broglie wavelength is calculated using the equation λ = h/mv, where λ is the wavelength, h is the Planck's constant, m is the mass, and v is the velocity. In this case, the mass and velocity of the Hubble Space Telescope are given. Plugging in the values into the equation, we get λ = (6.63 x 10^-34 m^2 kg / s) / (11,600 kg x 7.56 x 10^3 m/s) = 7.56 x 10^-42 m.