Open Question
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.
9. Quantum Mechanics
De Broglie Wavelength
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Calculate the de Broglie wavelength of a hydrogen atom traveling at 495 m/s. Assume the mass of a hydrogen atom is approximately 1.67 x 10^-27 kg.
A
2.67 x 10^-10 m
B
1.33 x 10^-10 m
C
5.01 x 10^-10 m
D
8.02 x 10^-10 m
Verified step by step guidance1
Identify the formula for the de Broglie wavelength: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant (6.626 x 10^-34 Js), \( m \) is the mass of the particle, and \( v \) is the velocity of the particle.
Substitute the given values into the formula: \( h = 6.626 \times 10^{-34} \) Js, \( m = 1.67 \times 10^{-27} \) kg, and \( v = 495 \) m/s.
Calculate the product of the mass and velocity: \( mv = (1.67 \times 10^{-27} \text{ kg}) \times (495 \text{ m/s}) \).
Divide Planck's constant by the product of mass and velocity to find the de Broglie wavelength: \( \lambda = \frac{6.626 \times 10^{-34} \text{ Js}}{mv} \).
Ensure the units are consistent and simplify the expression to find the wavelength in meters.
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