Please help with these Quantum theory Qs please

[Yuelao]

If someone could kindly spare some time and point out how to do these questions, most greatful.

1.After learning about de Broglie's hypothesis that particles of momentum, p, have wave characteristics with wavelength, h/p, a 76.00 kg student has grown concerned about being diffracted when passing through a doorway that is 85.00 cm wide. Assume that significant diffraction occurs when the width of the diffraction aperture is less than 10.0 times the wavelength of the wave being diffracted.

a) Determine the maximum speed at which the student can pass through the doorway so as to be significantly diffracted.
? m/s

b) With that speed, how long will it take the student to pass through the doorway if it is 15.0 cm thick?
? s



2. The resolving power of a microscope depends on the wavelength used. If one wished to use a microscope to "see" an atom, a resolution of about 15 pm (pico-meters) would have to be obtained.

a) If electrons are used (in an electron microscope), what minimum kinetic energy is required for the electrons? (Assume the electrons are non-relativistic.)
? eV

b) If photons are used, what minimum photon energy is needed to obtain the required resolution?
? eV


Thanks in advance~

 

[dextercioby]

If someone could kindly spare some time and point out how to do these questions, most greatful.

1.After learning about de Broglie's hypothesis that particles of momentum, p, have wave characteristics with wavelength, h/p, a 76.00 kg student has grown concerned about being diffracted when passing through a doorway that is 85.00 cm wide. Assume that significant diffraction occurs when the width of the diffraction aperture is less than 10.0 times the wavelength of the wave being diffracted.

a) Determine the maximum speed at which the student can pass through the doorway so as to be significantly diffracted.
? m/s

b) With that speed, how long will it take the student to pass through the doorway if it is 15.0 cm thick?
? s

The problem is rather stupid,but here goes:

a)His de Broglie's wavelength should be larger than 8,5cm ,which should correspond to a certain momentum.Knowing the momentum and mass of the diffracted body,u can find the speed.
b)Knowing the speed and length,u can simply find the time required.

2. The resolving power of a microscope depends on the wavelength used. If one wished to use a microscope to "see" an atom, a resolution of about 15 pm (pico-meters) would have to be obtained.

a) If electrons are used (in an electron microscope), what minimum kinetic energy is required for the electrons? (Assume the electrons are non-relativistic.)
? eV

b) If photons are used, what minimum photon energy is needed to obtain the required resolution?
? eV


Thanks in advance.

a)From de Broglie's formula,find the momentum and with the momentum and the mass,u can easily find the kinetic energy.
b)The same.If you have the wavelength,and knowing the speed of light and Planck's constant,u can easily find the energy.

 

[Yuelao]

ah~ pretty simple stuff, thanks for the advice, i'll go try do it now.