Part 1
An electron microscope operates with a beam of electrons, each of which has an energy of 20 KeV. Use the uncertainty principle in the form delta(x)delta(p) (greater or equal to) h/2 to find the smallest size that such a device could resolve. Planck's constant is 1.0552 × 10^-34 J · s. Answer in units of pm.

Part 2
What must the energy of each neutron in a beam of neutrons be in order to resolve the same size object?
Answer in units of eV.

Part 3
A beam of neutrons with a kinetic energy of 0.0002 eV falls on a slit of width 0.0001 m.
The Planck's constant is 6.63 × 10 ^-34 J · S.
What will be the angular spread of the beam after it passes through the slit?

Answer in units of radian.

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Hi C!

Here are the solutions to this problems set.

However, I must say I'm confused regarding the way the first problem is to be solved. It is stated that it should be solved using the uncertainty principle, while a more reasonable approach is the ...

Solution Summary

This solution provides step by step calculations for various questions involving Planck's constant.

Planck's formula for spectral distribution of the flux emitted by a blackbody is:
S_v = [(2*pi*h)/(c^2)][(v^3)/((e^hv/kT)-1)]
a) from this formula deduce that the totl flux is proportional to the fourth power of the temperture, that is:
integral from 0 to infinity S_v dv (proportionality symbo

If you body is emitting infrared radiation of wavelength 9.4 x 10^(-6)m, what is the energy of the released photons?
A hydrogen atom initially in the n =3 level emits a photon and ends up in the ground state.
a) What is the energy of the emitted photon?
b) If this atom then absorbs a second photon and returns to the n

Given: f(lambda) = 8pi*kt(lambda^4)
Where lambda is measured in meters, T is the temperature in kelvins, k is Boltzmann's constant. The Rayleigh-Jeans Law agrees with experimental measurements for long wavelengths but disagrees drastically for short wavelengths. [The law predicts that f(lambda) -> 0 as f(lambda) --> infinity

A certain rifle bullet has a mass of 8.13 g. Calculate the de Broglie wavelength of the bullet traveling at 1721 miles per hour. Physical constants are found below:
Physical Constants
Quantity Symbol Value
speed of light in a vacuum c 2.99792458Ã-108 m/s (exact)
Planck's con

See the attached file.
2. In the photoelectric effect experiment, light photons strike a photoelectric material in a phototube and electrons are emitted with a certain kinetic energy. If the stopping energy of the electrons is graphed as a function of the frequency of light, then the slope of the line will be Planck'sconstant

Part 1
Suppose optical radiation (of wavelength 2.6 × 10^-7 m) is used to determine the position of an electron to within the wavelength of the light. The mass of an electron is 9.10939 × 10^-31 kg and the Planck'sconstant is 6.62607 × 10^-34 J · s.
What will be the minimum resulting uncertainty in the electron's velocit

A beam of electrons (m=9.11 x 10 (-31) negative thirty first power has an average speed of 1.3 x 10^8 (eigth power) m*s (-1) s to to the negative first power. What is the wavelength of electrons having this average speed?
^=____________________________m
Assume your eyes receive a signal crossing of blue light, ^=470nm

A student performs a photoelectric experiment in which light of various frequencies is incident on a photosensitive metal plate. This plate, a second metal plate, and a power supply are connected in a circuit, which also contains two meters, M1 and M2, as shown above (see attachment, #1).
The student shines light of a specific

Prove that the De Broglie wavelength associated with a particle having kinetic energy K which is not negligible compared to its rest energy m_0 c^2 is given by
lemda = [h/(m_0 K)^(1/2)](1 + K/2m_0 c^2)^(-1/2)
The complete solution is in the attached file.