In order for a thermonuclear fusion reaction of two deuterons (2^1H^+) to take place, the deuterons must collide and each must have a velocity of about 1 * 10^6 m/s. Find the wavelength of such a deuteron.

Verified step by step guidance

1. Identify the formula to use: The de Broglie wavelength formula is \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \) m²kg/s), \( m \) is the mass of the particle, and \( v \) is the velocity.
2. Determine the mass of a deuteron: A deuteron is a nucleus of deuterium, consisting of one proton and one neutron. The mass of a deuteron is approximately \( 3.34 \times 10^{-27} \) kg.
3. Substitute the given velocity into the formula: The velocity \( v \) is given as \( 1 \times 10^6 \) m/s.
4. Plug the values into the de Broglie wavelength formula: \( \lambda = \frac{6.626 \times 10^{-34}}{3.34 \times 10^{-27} \times 1 \times 10^6} \).
5. Simplify the expression to find the wavelength \( \lambda \).