Question

Find the velocity of a neutron that has a 6.00-fm wavelength (about the size of a nucleus). Assume the neutron is nonrelativistic. (b) What is the neutron’s kinetic energy in MeV?

a) 1.52 x 10^6 m/s, 1.23 MeV
b) 2.86 x 10^6 m/s, 2.45 MeV
c) 4.13 x 10^6 m/s, 3.67 MeV
d) 5.49 x 10^6 m/s, 4.89 MeV

Answer 1

To find the velocity of a neutron with a 6.00-fm wavelength, use the de Broglie equation, v = h / (mλ). The velocity is approximately 1.52 x 10⁶ m/s. To find the kinetic energy, use the classical kinetic energy equation, KE = (1/2)mv². The kinetic energy is approximately 1.23 MeV.

Step-by-step explanation:

Given that the wavelength of a neutron is 6.00 fm (femtometers), we can use the de Broglie equation to find its velocity. The de Broglie equation states that the wavelength (λ) is equal to Planck's constant (h) divided by the mass (m) times the velocity (v): λ = h / (mv).

Rearranging the equation to solve for v, we get v = h / (mλ).

Using the given wavelength of 6.00 fm, we can calculate the velocity:

v = (6.626 × 10⁻³⁴ J s) / (mass of neutron * 6.00 × 10⁻¹⁵ m)

plugging in the mass of a neutron (1.675 × 10⁻²⁷ kg) gives:

v ≈ 1.52 × 10⁶ m/s

To find the kinetic energy of the neutron, we can use the classical kinetic energy equation: KE = (1/2)mv².

Plugging in the mass and velocity of the neutron gives:

KE = (1/2)(1.675 × 10⁻²⁷ kg)(1.52 × 10⁶ m/s)²

≈ 1.23 MeV.