Use the following figure for the next problem.
-The electrons coming out of the electron gun in an electron microscope are being accelerated by a potential of 100 kV.The wavelength of the electrons is
A)2.14 nm
B)3.88 pm
C)4.87 nm
D)12.4 pm
E)6.87 nm

Question

Use the following figure for the next problem. 
-The electrons coming out of the electron gun in an electron microscope are being accelerated by a potential of 100 kV.The wavelength of the electrons is
A)2.14 nm 
B)3.88 pm 
C)4.87 nm 
D)12.4 pm 
E)6.87 nm

Quizplus · Accepted Answer

The de Broglie wavelength of an electron accelerated by a potential difference V is given by λ = h/(√2meV), where h is the Planck's constant, me is the mass of electron, and V is the accelerating potential. Substituting h = 6.626 x 10^-34 J s, me = 9.109 x 10^-31 kg, and V = 100,000 V, we get:

λ = (6.626 x 10^-34 J s) / (√2 x 9.109 x 10^-31 kg x 100,000 V)
λ = 3.88 x 10^-12 m = 3.88 pm

Therefore, the correct choice is B) 3.88 pm.

Use the Following Figure for the Next Problem