Question

Part A

What is the wavelength of an electron of energy 25eV ?

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

?1 =

SubmitMy AnswersGive Up

Part B

What is the wavelength of an electron of energy 180eV ?

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

?2 =

SubmitMy AnswersGive Up

Part C

What is the wavelength of an electron of energy 1.0keV ?

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

?3 =

SubmitMy AnswersGive Up

Answer 1

Answer 2

A - 50 nm

句the 170 : 1240 cev

B- 6.9 nm

C- 1.2 nm

Answer 3

$A) E = hc / \lambda_{1} => 25 eV = ( 6.626*10^{-34} * 3*10^{8} ) / \lambda_{1}$

$=> \lambda_{1} = (6.626*10^{-34} * 3 * 10^{8}) / (25*1.6*10^{-19} ) = 49.70 nm$

$B) E = hc / \lambda_{2} => 180 eV = ( 6.626*10^{-34} * 3*10^{8} ) / \lambda_{2}$

$=> \lambda_{2} = (6.626*10^{-34} * 3 * 10^{8}) / (180*1.6*10^{-19} ) = 6.9 nm$

$C) E = hc / \lambda_{3} => 1000 eV = ( 6.626*10^{-34} * 3*10^{8} ) / \lambda_{3}$

$=> \lambda_{3} = (6.626*10^{-34} * 3 * 10^{8}) / (1000*1.6*10^{-19} ) = 1.24 nm$

Answer 4

wavelength = h/m*v

But we can write mv as sqrt((m/2)*K.e) (convert K.e from eV to J by multiplying by 1.60x10^-19)

mv = sqrt(9.11x10^-31/2*25ev*1.60x10^-19J/ev) =1.36*10^-24

wavelength = 6.63x10^-34/1.36*10^-24=0.4875nm

b) mv = sqrt(9.11x10^-31/2*180ev*1.60x10^-19J/ev) =3.4*10^-24

wavelength = 6.63x10^-34/3.4*10^-24=0.1967nm

c) mv = sqrt(9.11x10^-31/2*1000ev*1.60x10^-19J/ev) =.853*10^-24

wavelength = 6.63x10^-34/.853*10^-24=0.777nm

Answer 5

a)

The wavelenght of an electron of energy 25eV is,

$\lambda =\frac{h}{p}$

$\lambda =\frac{h}{\sqrt{2mE}}$

here,

$h=6.6\times 10^{-34} J.s$

$m=9.1\times 10^{-31} kg$

$\lambda =\frac{6.6\times 10^{-34}}{\sqrt{2(9.1\times 10^{-31})(25\times 1.6\times 10^{-19})}}$

$\lambda =\frac{6.6\times 10^{-34}}{\sqrt{728\times 10^{-50}}}$

$\lambda =\frac{6.6\times 10^{-34}}{26.98\times 10^{-25}}$

$\lambda =0.244\times 10^{-9} m$

${\color{Blue} \lambda =0.244 nm}$

b)

The wavelenght of an electron of energy 180eV is,

$\lambda =\frac{6.6\times 10^{-34}}{\sqrt{2(9.1\times 10^{-31})(180\times 1.6\times 10^{-19})}}$

$\lambda =\frac{6.6\times 10^{-34}}{\sqrt{5241.6\times 10^{-50}}}$

$\lambda =\frac{6.6\times 10^{-34}}{72.39\times 10^{-25}}$

$\lambda =0.091\times 10^{-9} m$

${\color{Blue} \lambda =91.1 pm}$

c)

The wavelenght of an electron of energy 1.0 keV is,

$\lambda =\frac{h}{p}$

$\lambda =\frac{6.6\times 10^{-34}}{\sqrt{2(9.1\times 10^{-31})(1000\times 1.6\times 10^{-19})}}$

$\lambda =\frac{6.6\times 10^{-34}}{\sqrt{29120\times 10^{-50}}}$

$\lambda =\frac{6.6\times 10^{-34}}{170.65\times 10^{-25}}$

$\lambda =0.038\times 10^{-9} m$

${\color{Blue} \lambda =38 pm}$