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

Answer:

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

Explanation:

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

$\lambda=\frac{h}{mv}$

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

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

electron:

mass = 9.1*10^{-31}kg

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

red light:

In this case you use the following formula:

$\lambda=\frac{c}{f}=\frac{3*10^8m/s}{4.3*10^{14}Hz}=6.97*10^{-7}m\approx700nm$

proton:

mass = 1.67*10^{-27}kg

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

car:

mass = 1500kg

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

baseball:

mass = 0.145kg

$\lambda=\frac{6.62*10^{-34}Js}{(0.145kg)(41m/s)}\\\\\lambda=1.11*10^{-34}m$

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

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

Answer 2

The arrangement of the objects from the largest wavelength to smallest wavelength is red light > electron = proton > baseball > car > person.

The given parameters;

• velocity of the person, v = 4.5 m/s
• speed of electron, v = 0.01c
• speed of red light, v = c
• speed of proton, v = 0.01 c
• speed of car, v = 27 m/s
• speed of baseball, v = 41 m/s.

where;

c is the speed of light = 3 x 10⁸ m/s.

The speed of the electron is calculated as follows;

$v_e = 0.01 \times 3\times 10^8 \ m/s\\\\v_e = 3\times 10^6 \ m/$

The speed of the red light is calculated as follows;

$v_r = c = 3\times 10^8 \ m/s$

The speed of the proton is calculated as follows;

$v_p = 0.01 \ c = 0.01 \times 3\times 10^8 \ m/s\\\\v_p = 3\times 10^6 \ m/$

The relationship between speed and wavelength is given as;

$v = f \lambda$

The object with the highest speed will have the largest wavelength.

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

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