What Limits Observation in Quantum Mechanics?

[blade_090]

1. Homework Statement [/b]
1)for an object of size 0.5 Angstrom, what is the longest-wavelength photon with which it can be observed?
2)for the object of problem 1, what is the smallest-energy electron which can be used to make the measurement?

Homework Equations

1)$$\Delta$$p x $$\Delta$$ x $$\geq$$ $$h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s$$/4(3.142)

2)$$\Delta$$E x $$\Delta$$ t $$\geq$$ $$h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s$$/4(3.142)

for problem 1,
0.5Angstrom is the wavelength.
i use the equation of E=hf to find the energy.
thn i use 2nd equation above to find $$\Delta$$ t
i use the $$\Delta$$ t $$\geq$$ [(lamda)^2]/4(pi)(speed of light)(delta lamda)
i did find the answer...bt somehow i feel like i did wrong

for problem 2,
i duno where i should start...
i tinking of using equation 2 bt I am not sure...whether energy equation from above is correct

the answer for prob 1 : 0.5Angstrom
the answer for prob 2 : 602eV

 

[ideasrule]

1. Homework Statement [/b]
1)for an object of size 0.5 Angstrom, what is the longest-wavelength photon with which it can be observed?
2)for the object of problem 1, what is the smallest-energy electron which can be used to make the measurement?

Homework Equations

1)$$\Delta$$p x $$\Delta$$ x $$\geq$$ $$h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s$$/4(3.142)

2)$$\Delta$$E x $$\Delta$$ t $$\geq$$ $$h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s$$/4(3.142)

for problem 1,
0.5Angstrom is the wavelength.
i use the equation of E=hf to find the energy.

No, 0.5A is the size of the object. You're supposed to find the wavelength of the photon. If you were trying to find the de Broglie wavelength of the object, you can't use E=hf because that only applies to photons.

Can you find the momentum of the photon? If so, what's the relationship between a photon's momentum and its wavelength?

for problem 2,
i duno where i should start...
i tinking of using equation 2 bt I am not sure...whether energy equation from above is correct

Once you find the momentum from problem 1, you can apply it to an electron. How do you find an electron's energy from its momentum?