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Multiple Choice
The faster an electron is moving, the _________ its kinetic energy, and the __________ its wavelength.
A
higher, shorter
B
higher, longer
C
lower, longer
D
lower, shorter
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Verified step by step guidance
1
Understand the relationship between an electron's speed and its kinetic energy. Kinetic energy is given by the formula: , where is the mass and is the velocity of the electron. As the velocity increases, the kinetic energy increases.
Consider the relationship between the speed of an electron and its wavelength. According to the de Broglie wavelength formula: , where is the wavelength, is Planck's constant, and is the momentum. Momentum is the product of mass and velocity, . As velocity increases, momentum increases, leading to a decrease in wavelength.
Analyze the options given in the problem. The correct relationship is that as the speed of an electron increases, its kinetic energy becomes higher and its wavelength becomes shorter.
Match the correct answer with the options provided. The correct choice is 'higher, shorter', which reflects the increase in kinetic energy and the decrease in wavelength as the electron's speed increases.
Review the concepts of kinetic energy and de Broglie wavelength to ensure understanding. Kinetic energy increases with speed, and wavelength decreases with increased momentum, which is directly related to speed.