Through what potential difference (Delta V) must electrons be accelerated ((From

Question

Through what potential difference (Delta V) must electrons be accelerated ((From rest) so that they will have the same wavelength as an X ray of wavelength 0.160 nm? Use 6.63*10^-34 for planks constant, 9.11*10^-31 kg for the mass of an electron, and 1.6*10^-19 for the change on an electrons. Thank you! Physics Hide

Mastering provides this response " Remember that the electron has the same de Broglie wavelength as the X ray, not the same energy" The answer should be around 55.3 V, as a problem with a wavelength of 0.165nm had this answer.

Explanation / Answer

The de broglie wavelength will be 0.16 nm for the electrons(given in the question)

now debroglie wavelength=h/p where h=6.626 * 10^-34 J-s and p is the momentun so putting h in the equation we get

p=h/(wavelength)=4.14*10^-24 kgm/s also p=sqrt(2mE) =>sqrt(2mE)=4.14*10^-24 where E is the energy and m is the mass of electrons

so E=58.89 eV is the energy..now the voltage required will be thus E/q=58.89 V is the answer

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