Use the References to access important values if needed for this question. Compa

Question

Use the References to access important values if needed for this question. Compare the de Broglie wavelength of a baseball 1.30x10 miles per hour (5.81x10° m/s) and a golf ball with a speed of 70.0 miles per hour (31.3 m/s) moving at 90.0 miles per hour (40.2 m/s) to that of an electron moving at Louis de Broglie Which region of the electromagnetic spectrum are each of these wavelengths near? A. Ultraviolet 10 to 10 meters B. X-ray C. Gamma ray to 10 meters D. Smallerthan meters. Cannot detect wave-like properties. Only particle-like behavior will be observable. 101 to 108 meters c. Gamma ray 10 to 10' meters Particle Mass (kg) Velocity (m/s) Wavelength (m) Region baseball electron 9.11x10 5.81x10 golf ball 4.50x102 Particle 0.140 40.2 31.3 Submit Answer Nod

Explanation / Answer

Particle : Baseball

kinetic energy (E) = (1/2)mv^2

Feed m = mass and v = velocity from above

E = (1/2) x 0.140 x (40.2)^2 = 113.123 J

wavelength (l) = h/p = h/sq.rt.(2Em)

h = planck's constant

wavelength of particle = 6.626 x 10^-34/sq.rt.(2 x 0.140 x 113.123) = 1.18 x 10^-34 m

Region : Particle like behavior only.

Particle : Electron

kinetic energy (E) = (1/2)mv^2

Feed m = mass and v = velocity from above

E = (1/2) x 9.11 x 10^-31 x (5.81 x 10^6)^2 = 1.54 x 10^-17 J

wavelength (l) = h/p = h/sq.rt.(2Em)

h = planck's constant

wavelength of particle = 6.626 x 10^-34/sq.rt.(2 x 9.11 x 10^-31 x 1.54 x 10^-17) = 1.25 x 10^-10 m

Region : X-ray

Particle : Golf ball

kinetic energy (E) = (1/2)mv^2

Feed m = mass and v = velocity from above

E = (1/2) x 4.50 x 10^-2 x (31.3)^2 = 22.04 J

wavelength (l) = h/p = h/sq.rt.(2Em)

h = planck's constant

wavelength of particle = 6.626 x 10^-34/sq.rt.(2 x 4.50 x 10^-2 x 22.04) = 4.70 x 10^-34 m

Region : Particle like only

Particle : Bullet

kinetic energy (E) = (1/2)mv^2

Feed m = mass and v = velocity from above

E = (1/2) x 1.90 x 10^-3 x (31.3)^2 = 0.931 J

wavelength (l) = h/p = h/sq.rt.(2Em)

h = planck's constant

wavelength of particle = 6.626 x 10^-34/sq.rt.(2 x 1.90 x 10^-3 x 0.931) = 1.11 x 10^-32 m

Region : Particle like only

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