Questions: Calculate the wavelength of a neutron traveling at 2.65 x 10^5 m/s. Mass of neutron is 1.67 x 10^-27 kg.

Solution Steps

To find the wavelength of a neutron, we use the de Broglie wavelength formula:

\[ \lambda = \frac{h}{mv} \]

where:

• \(\lambda\) is the wavelength,
• \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{m}^2 \, \text{kg/s}\)),
• \(m\) is the mass of the neutron (\(1.67 \times 10^{-27} \, \text{kg}\)),
• \(v\) is the velocity of the neutron (\(2.65 \times 10^5 \, \text{m/s}\)).

Substitute the given values into the de Broglie wavelength formula:

\[ \lambda = \frac{6.626 \times 10^{-34}}{(1.67 \times 10^{-27}) \times (2.65 \times 10^5)} \]

Calculate the denominator:

\[ (1.67 \times 10^{-27}) \times (2.65 \times 10^5) = 4.4255 \times 10^{-22} \]

Now, calculate the wavelength:

\[ \lambda = \frac{6.626 \times 10^{-34}}{4.4255 \times 10^{-22}} = 1.497 \times 10^{-12} \, \text{m} \]

Final Answer