Question

A brave student is attempting to come to class in a car weighing 2,200 pounds and driving at 140 mph (the end of the speedometer) so he can be on time. Calculate the wavelength of the car at the top speed of 140 mph. Why would you NOT wish to use wave mechanics to describe the motion of a particle such as this?

Answer 1

Answer:
`\lambda =2.1* 10^(-38) m`

Step-by-step explanation:

Given

weight of car
`=2200 Pounds\approx 997.90 kg`

Velocity of car
`=140 mph\approx 62.58 m/s`

Energy conservation

`(mv^2)/(2)=h\\u`

where h=planck constant

`\\u =(mv^2)/(2h)`

`\\u =(997.90* 62.58^2)/(2* 6.626* 10^(-34))`

`\\u =294901.3 * 10^(-34) s^(-1)`

Now wavelength

`\lambda =(v)/(\\u )`

`\lambda =(62.58)/(294901.3 * 10^(-34))`

`\lambda =2.1* 10^(-38) m`

We do not use the wave mechanics because the size of the particle and wavelength are not comparable.