PLEASE ANSWER CORRECTLY AND I WILL RATE HIGH Part A 1) Calculate the de Broglie

Question

PLEASE ANSWER CORRECTLY AND I WILL RATE HIGH

Part A

1) Calculate the de Broglie wavelength of an electron if it is accelerated from rest by 33000 V as in the figure above. Suppose that the electron is relativistic if its kinetic energy is greater than 1% of the electron rest energy. Express your answer to two significant figures and include the appropriate units.

2) A typical gamma ray emitted from a nucleus during radioactive decay may have an energy of310 keV

What is its wavelength?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

1)

The de Broglie wavelength of the electron is,

= h/ (sqrt (2meV))

where h= Planck’s constant (6.625x10-34)

m= mass of electron (9.11x10-31)

e= charge of electron (1.6x10-19)

V= 33000V

= (6.625x10-34)/ (sqrt (2(9.11x10-31)(1.6x10-19)(33000))

=6.755x10-12m or 6.755 pm

2)

Wavelength () = hc/E

hc= 1240eV nm

E= 310keV

= hc/ E =[ (1240eV nm) / (310x103)]=4.0x10-3 m

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