Question

Rank these objects on the basis of their wavelength. (largest to smallest)

person v=4.5m/s
electron v=0.01c
red light v=c
proton v=0.01c
car v=27m/s
baseball v=41m/s

Answer 1

The concepts used to solve this problem are de Broglie wavelength.

Initially, use the concept of de Broglie wavelength to find the wavelength of the person, electron, red light, proton, car, and baseball.

Finally, use the obtained wavelength of the person, electron, red light, proton, car, and baseball to rank the objects on the basis of their wavelength.

The expression for de Broglie wavelength is given below:

Here, is the wavelength, is Planck’s constant, is the velocity of the particle, and is the mass of the particle.

The expression for de Broglie wavelength is given below:

For the wavelength of a person:

The expression for de Broglie wavelength in terms of average mass of a person is given below:

Here, the wavelength of a person is , average mass of a person is , and speed of a person is .

Substitute for , for , and for .

                                                                 …… (1)

For the wavelength of an electron:

The expression for de Broglie wavelength in terms of average mass of an electron is given below:

Here, the wavelength of an electron is , the average mass of an electron is , and the speed of an electron is .

Substitute for , for , and for .

Substitute for .

                                             …… (2)

For the wavelength of a red light:

The wavelength of red light is as follows:

                                                                           …… (3)

Here, the wavelength of red light is .

For the wavelength of a proton:

The expression for de Broglie wavelength in terms of average mass of a proton is given below:

Here, the wavelength of a proton is , average mass of a proton is , and speed of a proton is .

Substitute for , for , and for .

Substitute for .

                                          …… (4)

For the wavelength of a car:

The expression for de Broglie wavelength in terms of the average mass of a car is given below:

Here, the wavelength of a car is , average mass of a car is , and speed of a car is .

Substitute for , for , and for .

                                                                    …… (5)

For the wavelength of a baseball:

The expression for de Broglie wavelength in terms of average mass of a baseball is given below:

Here, the wavelength of a baseball is , average mass of a baseball is , and speed of a baseball is .

Substitute for , for , and for .

                                                                …… (6)

From the above step:

The wavelength of a person is .

The wavelength of an electron is .

The wavelength of a red light is .

The wavelength of a proton is .

The wavelength of a car is .

The wavelength of a baseball is .

The order of the given data is arranged from largest to smallest on the basis of wavelength as follows:

Red light, electron, proton, baseball, person, and car.

The rank of the objects arranged on the basis of their wavelength from largest to smallest is Red light, electron, proton, baseball, person, and car.