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X rays with a wavelength of 1.54 times 10^-10 m are produced when a copper metal

ID: 519700 • Letter: X

Question

X rays with a wavelength of 1.54 times 10^-10 m are produced when a copper metal target is bombarded with high-energy electrons that have been accelerated by a voltage difference of 30,000 V. The kinetic energy of the electrons equals the product of the voltage difference and the electronic charge in coulombs, where 1 volt-coulomb = 1J. (a) What is the kinetic energy in joules and the de Broglie wavelength in meters of an electron that has been accelerated by a voltage difference of 30,000 V? (b) What is the energy in joules of the X rays emitted by the copper target?

Explanation / Answer

a) Kinetic energy = Volt × Coulomb

= 30000 v × 1.602×10^-19coulombs

= 4.81×10^-15 Volt -Coulomb

= 4.81×10^-15 J

De Broglie wavelength = h/2Em

= 6.626×10^-34J.s/2×4.81×10^-15J × 9.109× 10^-31Kg

= 7.08 ×10^-12m

b) E = hv

frequency ,v = speed of light/wave length

= 2.99 × 10^8(m/s )/1.54×10^-10m

= 1.94 × 10^18 / s

E = 6.626 ×10^-34Js × 1.94 × 10^18s^-1

= 1.29 × 10^-15 J