Calculate the energy of a neutron whose de Broglie wavelength is 0.7 Å. Assume the mass of the neutron is 1.675 x 10^-27 kg and use Planck's constant h = 6.626 x 10^-34 J·s.

• A. 3.8 x 10^-21 J
• B. 7.4 x 10^-23 J
• C. 5.6 x 10^-22 J
• D. 1.2 x 10^-20 J

Answer: (A)

Verified step by step guidance

1. Start by understanding the de Broglie wavelength formula: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant, \( m \) is the mass, and \( v \) is the velocity of the particle.
2. Rearrange the de Broglie equation to solve for velocity \( v \): \( v = \frac{h}{m\lambda} \). Substitute the given values: \( h = 6.626 \times 10^{-34} \) J·s, \( m = 1.675 \times 10^{-27} \) kg, and \( \lambda = 0.7 \times 10^{-10} \) m (since 1 Å = 10^{-10} m).
3. Calculate the velocity \( v \) using the rearranged formula: \( v = \frac{6.626 \times 10^{-34}}{1.675 \times 10^{-27} \times 0.7 \times 10^{-10}} \).
4. Once you have the velocity, use the kinetic energy formula \( KE = \frac{1}{2}mv^2 \) to find the energy of the neutron. Substitute the mass \( m = 1.675 \times 10^{-27} \) kg and the calculated velocity \( v \).
5. Calculate the kinetic energy \( KE \) using the formula: \( KE = \frac{1}{2} \times 1.675 \times 10^{-27} \times v^2 \). This will give you the energy of the neutron in joules.