Question

Rank these objects on the basis of their wavelength. (largest to smallest)person v=4.5m/selectron v=0.01cred light v=cproton v=0.01ccar v=27m/sbaseball v=41m/s

Answer 1

red light > electron > proton > baseball > person > car

Step-by-step explanation:

To calculate the wavelength associated to each object, you use the Broglie's relation:

`\lambda=(h)/(mv)\\\\`

h: Planck,s constant = 6.62*10^-34 Js

m: mass

v: velocity

For each object you use an average values of its mass.

person:

mass = 80kg

`\lambda=(6.62*10^(-34)Js)/((80kg)(4.5m/s))=1.83*10^(-36)m`

electron:

mass = 9.1*10^{-31}kg

`\lambda=(6.62*10^(-34)Js)/((9.1*10^(-31)kg)(0.01c))\\\\\lambda=(6.62*10^(-34)Js)/((9.1*10^(-31)kg)(0.01(3*10^(8)m/s)))\\\\\lambda=2.42*10^(-10)m`

red light:

In this case you use the following formula:

`\lambda=(c)/(f)=(3*10^8m/s)/(4.3*10^(14)Hz)=6.97*10^(-7)m\approx700nm`

proton:

mass = 1.67*10^{-27}kg

`\lambda=(6.62*10^(-34)Js)/((1.67*10^(-27)kg)(0.01(3*10^8m/s)))\\\\\lambda=1.32*10^(-13)m`

car:

mass = 1500kg

`\lambda=(6.62*10^(-34)Js)/((1500kg)(27m/s))=1.63*10^(-38)m`

baseball:

mass = 0.145kg

`\lambda=(6.62*10^(-34)Js)/((0.145kg)(41m/s))\\\\\lambda=1.11*10^(-34)m`

hence, by comparing the wavelengths of the objects you have:

red light > electron > proton > baseball > person > car