9. Quantum Mechanics
De Broglie Wavelength
2PRACTICE PROBLEM
When high-energy electrons that have been accelerated by a voltage difference of 25,000 V bombard a metal sample target, X rays with a wavelength of 1.74×10−10 m are created. The product of the voltage difference and the electronic charge, expressed in coulombs, yields the kinetic energy of the electrons, where 1 volt-coulomb equals 1 J. What are the electron's kinetic energy in joules and de Broglie wavelength in meters when accelerated by a 25,000 V voltage difference?
When high-energy electrons that have been accelerated by a voltage difference of 25,000 V bombard a metal sample target, X rays with a wavelength of 1.74×10−10 m are created. The product of the voltage difference and the electronic charge, expressed in coulombs, yields the kinetic energy of the electrons, where 1 volt-coulomb equals 1 J. What are the electron's kinetic energy in joules and de Broglie wavelength in meters when accelerated by a 25,000 V voltage difference?
ANSWERS OPTIONS
A
The electron's kinetic energy is 4.01×10−15 J and the de Broglie wavelength is 7.76×10−12 m.
B
The electron's kinetic energy is 1.56×1023 J and the de Broglie wavelength is 4.96×10−11 m.
C
The electron's kinetic energy is 1.61×10−19 J and the de Broglie wavelength is 1.14×10−15 m.
D
The electron's kinetic energy is 1.61×10−19 J and the de Broglie wavelength is 8.77×1014 m.