A neutron has a mass of 1.67 × 10−²⁷ kg. The de Broglie wavelength is 1.4 × 10−¹⁰ m. How fast is the neutron going? (in m/s)

Question

Quizplus · Accepted Answer

The de Broglie wavelength is given by the formula $\lambda = \frac{h}{p}$, where $h$ is Planck's constant, and $p$ is the momentum of the particle.

In this case, we are given the de Broglie wavelength $\lambda$ and the mass $m$ of the neutron. We can use the formula $p=\frac{h}{\lambda}$ to find the momentum of the neutron:

$p=\frac{h}{\lambda}=\frac{6.626 	imes 10^{-34}~	ext{J s}}{1.4 	imes 10^{-10}~	ext{m}} \approx 4.732 	imes 10^{-24}~	ext{kg}\;	ext{m/s}$

Finally, we can use the definition of momentum to find the velocity of the neutron:

$p = mv \quad \Rightarrow \quad v = \frac{p}{m} = \frac{4.732 	imes 10^{-24}~	ext{kg}\;	ext{m/s}}{1.67 	imes 10^{-27}~	ext{kg}} \approx 2.825~	imes 10^3~	ext{m/s}$

Thus, the answer is B, 2.8 × 10^3 m/s.

A Neutron Has a Mass of 1