Question

Calculate the de Broglie wavelength of an electron and a one-ton car, both moving with speed of 100 km/hour. Based on your calculation could you predict which will behave like a "quantum particle" and why. Please explain each step in words and detail.

Answer 1

(a). The wavelength of electron is 26.22 μm.

(b).The wavelength of car is
`2.38*10^(-38)\ m`

Explanation :

Given that,

Speed = 100 km/hr

Mass of car = 1 ton

(a). We need to calculate the wavelength of electron

Using formula of wavelength

`\lambda_(e)=(h)/(p)`

`\lambda_(e)=(h)/(mv)`

Put the value into the formula

`\lambda_(e)=(6.63*10^(-34))/(9.1*10^(-31)*100*(5)/(18))`

`\lambda=0.00002622`

`\lambda=26.22*10^(-6)\ m`

`\lambda=26.22\ \mu m`

(II). We need to calculate the wavelength of car

Using formula of wavelength again

`\lambda_(e)=(6.63*10^(-34))/(1000*100*(5)/(18))`

`\lambda=2.38*10^(-38)\ m`

The wavelength of the electron is greater than the dimension of electron and the wavelength of car is less than the dimension of car.

Therefore, electron is quantum particle and car is classical.

Hence, (a). The wavelength of electron is 26.22 μm.

(b).The wavelength of car is
`2.38*10^(-38)\ m`.